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

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

G. C. Greubel, Table of n, a(n) for n = 2..1000

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, arXiv:0910.4676 [math.NT], 2009.

Mathematica

RecurrenceTable[{a[n] == a[n - 1] + GCD[n, a[n - 1]], a[2] == 3}, a, {n, 2, 100}] (* G. C. Greubel, Jun 05 2016 *)

Crossrefs

Cf. A167170, A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.

Sequence in context: A278489 A191880 A084020 * A032489 A153769 A275608

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