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A039654
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a(n) = prime reached by iterating f(x) = sigma(x)-1 starting at n, or -1 if no prime is ever reached.
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21
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2, 3, 11, 5, 11, 7, 23, 71, 17, 11, 71, 13, 23, 23, 71, 17, 59, 19, 41, 31, 47, 23, 59, 71, 41, 71, 71, 29, 71, 31, 167, 47, 53, 47, 233, 37, 59, 71, 89, 41, 167, 43, 83, 167, 71, 47, 167, 167, 167, 71, 97, 53, 167, 71, 167, 79, 89, 59, 167, 61, 167, 103, 311, 83, 167, 67
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OFFSET
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2,1
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COMMENTS
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It appears nearly certain that a prime is always reached for n>1.
Since sigma(n) > n for n > 1, and sigma(n) = n + 1 only for n prime, the iteration either reaches a prime and loops there, or grows indefinitely. - Franklin T. Adams-Watters, May 10 2010
Guy (2004) attributes this conjecture to Erdos. See Erdos et al. (1990). - N. J. A. Sloane, Aug 30 2017
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. See Section B41, p. 149.
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LINKS
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N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)
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MATHEMATICA
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f[n_] := DivisorSigma[1, n]-1; Table[FixedPoint[f, n], {n, 2, 100}] (* T. D. Noe, May 10 2010 *)
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PROG
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CROSSREFS
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Cf. A039655 (the number of steps needed), A039649, A039650, A039651, A039652, A039653, A039656, A291301, A291302, A291776, A291777.
Cf. A177343: number of times the n-th prime occurs in this sequence.
Cf. A292874: least k such that a(k) = prime(n).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Changed escape value from 0 to -1 to be consistent with several related sequences. - N. J. A. Sloane, Aug 31 2017
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STATUS
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approved
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