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A066421
a(n) = least k > 0 such that sigma^(k)(n) + 1 is prime, if such k exists; otherwise 0, where sigma^(k) denotes application of sigma k times.
4
1, 2, 1, 5, 1, 1, 4, 3, 4, 1, 1, 1, 3, 2, 2, 5, 1, 5, 2, 1, 4, 1, 2, 1, 5, 1, 1, 4, 1, 1, 4, 3, 9, 4, 9, 2, 2, 1, 4, 3, 1, 1, 9, 8, 1, 1, 9, 8, 5, 4, 1, 5, 4, 3, 1, 3, 4, 3, 1, 4, 2, 1, 2, 4, 8, 3, 2, 1, 1, 3, 1, 2, 3, 2, 8, 2, 1, 4, 4, 3, 4, 1, 8, 7, 1, 2, 3, 1, 3, 2, 1, 4, 3, 3, 3, 4, 5, 4, 1, 2
OFFSET
1,2
COMMENTS
Does the orbit of the arithmetical dynamical system f(n) = sigma(n) contain one less than a prime, for every initial point n? That is to say, is a(n) nonzero for every n?
a(n) > 0 for all n < 36090. If a(36090) > 0, it is > 159. - Gabriel Cunningham (gcasey(AT)mit.edu), Oct 15 2004
a(n) > 0 for all n <= 675000 and a(36090)=291. - Sean A. Irvine, Oct 15 2023
LINKS
EXAMPLE
sigma(sigma(sigma(8))) + 1 = sigma(sigma(15)) + 1 = sigma(24) + 1 = 60 + 1 = 61, a prime; hence a(8) = 3.
MATHEMATICA
A066421[n_]:=Length[NestWhileList[DivisorSigma[1, #]&, DivisorSigma[1, n], !PrimeQ[#+1]&]]; Array[A066421, 100] (* Paolo Xausa, Oct 16 2023 *)
PROG
(PARI) A066421(n) = { my(k=1, s=sigma(n)); while(!isprime(1+s), k++; s = sigma(s)); k; }; \\ Antti Karttunen, Nov 07 2017
CROSSREFS
Sequence in context: A348494 A256541 A342919 * A369526 A206563 A299779
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 26 2001
EXTENSIONS
More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Oct 15 2004
Description clarified by Antti Karttunen, Nov 07 2017
STATUS
approved