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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

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

EXAMPLE

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

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

Cf. A099433, A099434.

Sequence in context: A078036 A175178 A256541 * A206563 A299779 A323954

Adjacent sequences:  A066418 A066419 A066420 * A066422 A066423 A066424

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

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Last modified May 30 15:38 EDT 2020. Contains 334726 sequences. (Running on oeis4.)