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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 Rowland-like "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 prime-generating 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[n-1] + igcd(n, A[n-1]) 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

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Last modified December 13 15:03 EST 2018. Contains 318086 sequences. (Running on oeis4.)