A167195 - OEIS

This site is supported by donations to The OEIS Foundation.

A167195

a(2)=3, for n>=3, a(n)=a(n-1)+gcd(n, a(n-1))

3, 6, 8, 9, 12, 13, 14, 15, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 44, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 92, 93, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`2,1`
	COMMENTS	`For every n>=3, a(n)-a(n-1) is 1 or prime. This Rowland-like "generator of primes" is different from A106108 and from generators A167168. Generalization: Let p be a prime. Let N(p-1)=p and for n>=p, N(n)=N(n-1)+gcd(n, N(n-1)). Then, for every n>=p, N(n)-N(n-1) is 1 or prime.`
	LINKS	`Table of n, a(n) for n=2..68.` `E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008), Article 08.2.8` `V. Shevelev, A new generator of primes based on the Rowland idea`
	CROSSREFS	`Cf. A167170 A167168 A106108 A132199 A167054 A167053 A166944 A166945 A116533 A163961 A163963 A084662 A084663 A134162 A135506 A135508 A118679 A120293` `Sequence in context: A188028 A191880 A084020 * A032489 A153769 A155723` `Adjacent sequences: A167192 A167193 A167194 * A167196 A167197 A167198`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vladimir Shevelev, Oct 30 2009, Nov 06 2009`
	EXTENSIONS	`Edited by Charles R Greathouse IV, Nov 02 2009`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified June 20 02:04 EDT 2013. Contains 226416 sequences.