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A066421
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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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4
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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sigma(sigma(sigma(8))) + 1 = sigma(sigma(15)) + 1 = sigma(24) + 1 = 60 + 1 = 61, a prime; hence a(8) = 3.
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MATHEMATICA
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A066421[n_]:=Length[NestWhileList[DivisorSigma[1, #]&, DivisorSigma[1, n], !PrimeQ[#+1]&]]; Array[A066421, 100] (* Paolo Xausa, Oct 16 2023 *)
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PROG
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(PARI) A066421(n) = { my(k=1, s=sigma(n)); while(!isprime(1+s), k++; s = sigma(s)); k; }; \\ Antti Karttunen, Nov 07 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Oct 15 2004
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STATUS
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approved
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