Investigators believe a note found in the Las Vegas shooter’s hotel room contained a series of numbers that helped him calculate more precise shots.

A law enforcement official said on Saturday that the numbers found on a note on a nightstand included the distance between the high-rise hotel room that Stephen Paddock was using as a perch and the concert the victims were attending.

The official wasn’t authorised to discuss the details of the investigation publicly and spoke to The Associated Press on condition of anonymity.

Investigators are still trying to determine why Paddock committed the deadliest mass shooting in modern US history.

The alleged note containing calculations can be seen on a nightstand in photos taken by investigators. Photo: Twitter

He killed 58 people and wounded hundreds of others last Sunday before taking his own life.

Earlier on Saturday, US Vice President Mike Pence spoke at a prayer service in Las Vegas honouring the 58 victims killed last Sunday.

Mr Pence says those killed were taken before their time. But he says: “Their names and their stories will forever be etched into the hearts of the American people.”

Fifty-eight doves were released outside on the steps of City Hall. They flew in a wide arc before disappearing into the distance as someone shouted, “God bless America!”

Baffled police and FBI agents, still lacking a clear motive for the Las Vegas massacre of 58 people by a lone gunman five days ago, have appealed to the public to come forward with any information that might help solve the mystery.

Clark County Undersheriff Kevin McMahill said investigators have, to no avail, run down more than 1000 leads seeking clues to what drove a 64-year-old wealthy retiree with a penchant for gambling to carry out the deadliest mass shooting in modern US history.

Paddock fired a barrage of gunfire from the windows of his 32nd-floor hotel suite into a crowd of 20,000 people attending an outdoor music festival on Sunday night, then killed himself before police stormed his room.

People take cover at the Route 91 Harvest country music festival. Photo: Getty

In addition to the 58 people killed, nearly 500 were injured, some by gunfire, some trampled or otherwise hurt while running for cover.

Unlike so many other perpetrators of deadly mass shootings before him, Paddock left behind no suicide note, no manifesto, no recordings and no messages on social media pointing to his intent, according to police.

“We have looked at everything, literally, to include the suspect’s personal life, any political affiliation, his social behaviours, economic situation, any potential radicalisation,” Mr McMahill told reporters.

“We are looking at every aspect from birth to death of this suspect and this case.”

Mr McMahill acknowledged that Islamic State had repeatedly claimed responsibility for the attack, but said investigators had uncovered “no nexus” between that Mideast-based militant group and Paddock.

In an unusual bid to cast a wider net for additional tips, the FBI and police have arranged with communications company Clear Channel to post billboards around Las Vegas urging members of the public to come forward with any information they believe might help investigators.

The billboards will bear the slogan “If you know something, say something”, and carry a toll-free number to an FBI hotline.

Mr McMahill said investigators were satisfied that no one else was in the room with Paddock, who checked into the Mandalay Bay hotel three days before the massacre.

But police suspect Paddock may have had assistance at some point before the killings, based on the large number of guns, ammunition and explosives that were found in the hotel suite, his home, his car and a second home searched in Reno.

Police consider Marilou Danley a person of interest. Photo: AAP

Authorities have said that 12 of the weapons recovered from Paddock’s hotel suite were equipped with so-called bump-stock devices that enable semi-automatic rifles to be operated as if they were fully automatic machine-guns.

Paddock’s ability to fire hundreds of rounds per minute over the course of his 10-minute shooting spree was a major factor in the high casualty count, police said.

The National Rifle Association, the influential gun lobby that has staunchly opposed moves to tighten firearms control laws after previous mass shootings, came out on Thursday in favour of placing new regulations on bump stock accessories.

Reports have emerged in recent days that Paddock may have targeted other sites for attack in Las Vegas, Chicago or Boston before Sunday’s shooting, which police have said they were investigating.

Paddock’s girlfriend, Marilou Danley, 62, was questioned by the FBI on Wednesday and said in a statement she never had any inkling of Paddock’s plans.

Danley, who returned to the US late on Tuesday from a family visit to the Philippines, is regarded by investigators as a “person of interest”.

The Australian citizen of Filipino heritage is co-operating with authorities, her lawyer said.