

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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. (From Alonso del Arte, Nov 30 2009)


REFERENCES

E. S. Rowland, A natural primegenerating recurrence, Journal of Integer Sequences, Volume 11 (2008), Issue 2, Article 8


LINKS

G. C. Greubel, Table of n, a(n) for n = 6..1000
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



