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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, 117, 120, 121, 122, 123, 124, 125, 126, 127, 128 (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 1's. [Alonso del Arte, Nov 30 2009]
LINKS
E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, 11 (2008), Article 08.2.8.
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}]
PROG
(Python)
from math import gcd
def aupton(nn):
alst = [7]
for n in range(7, nn+1): alst.append(alst[-1] + gcd(n, alst[-1]))
return alst
print(aupton(68)) # Michael S. Branicky, Jul 14 2021
CROSSREFS
Sequence in context: A115770 A086779 A269173 * A336797 A100599 A353440
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 March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)