

A167197


a(6) = 7, for n >= 7, a(n) = a(n  1) + gcd(n, a(n  1))


6



7, 14, 16, 17, 18, 19, 20, 21, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 116
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OFFSET

6,1


COMMENTS

For every n >= 7, a(n)  a(n  1) is 1 or prime. This Rowlandlike "generator of primes" is different from A106108 (see comment to A167168) and from A167170. Note that, lim sup a(n) / n = 2, while lim sup A106108(n) / n = lim sup A167170(n) / n = 3.
Going up to a million, differences of two consecutive terms of this sequence gives primes about 0.009% of the time. The rest are 1s. [Alonso del Arte, Nov 30 2009]


LINKS

G. C. Greubel, Table of n, a(n) for n = 6..1000
E. S. Rowland, A natural primegenerating recurrence, Journal of Integer Sequences, 11 (2008), Article 08.2.8.
V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009.


MAPLE

A[6]:= 7:
for n from 7 to 100 do A[n]:= A[n1] + igcd(n, A[n1]) od:
seq(A[i], i=6..100); # Robert Israel, Jun 05 2016


MATHEMATICA

a[6] = 7; a[n_ /; n > 6] := a[n] = a[n  1] + GCD[n, a[n  1]]; Table[a[n], {n, 6, 58}]


CROSSREFS

Cf. A167195, A167170, A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.
Sequence in context: A115770 A086779 A269173 * A100599 A198390 A118905
Adjacent sequences: A167194 A167195 A167196 * A167198 A167199 A167200


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Oct 30 2009, Nov 06 2009


EXTENSIONS

Verified and edited by Alonso del Arte, Nov 30 2009


STATUS

approved



