A099433 -id:A099433 - cp's OEIS frontend

A099434 a(n) = A066421(A099433(n)). The value of A066421 on its record-holders.

Original entry on oeis.org

1, 2, 5, 9, 12, 13, 14, 30, 37, 291, 292

Offset: 1

Gabriel Cunningham (gcasey(AT)mit.edu), Oct 15 2004

Cf. A066421, A099433.

Offset corrected and a(10)-a(11) added by Amiram Eldar, Apr 11 2025

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.

Original entry on oeis.org

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

Joseph L. Pe, Dec 26 2001

nonn

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

			sigma(sigma(sigma(8))) + 1 = sigma(sigma(15)) + 1 = sigma(24) + 1 = 60 + 1 = 61, a prime; hence a(8) = 3.

Antti Karttunen, Table of n, a(n) for n = 1..36089

Cf. A099433, A099434.

A066421[n_]:=Length[NestWhileList[DivisorSigma[1,#]&,DivisorSigma[1,n],!PrimeQ[#+1]&]];Array[A066421,100] (* Paolo Xausa, Oct 16 2023 *)

A066421(n) = { my(k=1,s=sigma(n)); while(!isprime(1+s),k++;s = sigma(s)); k; }; \\ Antti Karttunen, Nov 07 2017

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Oct 15 2004

Description clarified by Antti Karttunen, Nov 07 2017

cp's OEIS Frontend

A099434 a(n) = A066421(A099433(n)). The value of A066421 on its record-holders.

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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.

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