A reward of up to £3,000 is being offered for information leading to the arrest and conviction of a "dangerous and predatory individual" who is suspected to have committed a serious sex offence while on the run.
Ivan Leach, also known as Lee Cyrus, 47, went missing from North Sea Camp open prison in Boston, Lincolnshire, after he failed to return from day release on October 9.
The public are warned not to approach him under any circumstances as he poses a significant risk.
He is believed to have carried out a very serious sexual attack in Tayside, Scotland, since he absconded although further details cannot be released for legal reasons, said Lancashire Police.
Leach was born in Preston, Lancashire, and has connections across the city as well as in South Ribble.
It is known he has been in the city on a number of occasions since he absconded, but he could be anywhere in the country, police said.
Today the Crimestoppers charity has offered a cash reward up to £3,000 for information leading to an arrest and conviction.
Detective Superintendent Paul Withers, of Lancashire Police Force's Major Investigation Team, said:
The last confirmed sighting of Leach is on the evening of Friday, October 19 in Lea, Preston, but despite a nationwide appeal he remains at large.
Inquiries are ongoing in Nottinghamshire, Lincolnshire and Tayside.
Lancashire Police are also investigating reports that two schoolgirls were approached as they sat at a bus stop around 6.30pm on Lancaster Road in Preston city centre on Wednesday, October 17.
The girls were approached by a man matching Leach's description who made sexual remarks towards them and encouraged them to participate in sexual acts with him.
The girls boarded their bus and reported the incident to the police.
Leach was jailed in 2005 for robbing a 90-year-old woman in her home in Ribbleton, Preston.
He was given a life sentence with a minimum tariff of five years. He also has convictions for burglary and robbery and assault.