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 A039654 a(n) = prime reached by iterating f(x) = sigma(x)-1 starting at n, or -1 if no prime is ever reached. 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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 REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004. See Section B41, p. 149. LINKS Franklin T. Adams-Watters, Table of n, a(n) for n=2..10000 Lucilla Baldini and Josef Eschgfäller, Random functions from coupled dynamical systems, arXiv preprint arXiv:1609.01750 [math.CO], 2016. Mentions the conjecture. Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers] 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) MATHEMATICA f[n_]:=Plus@@Divisors[n]-1; Table[Nest[f, n, 6], {n, 2, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *) f[n_] := DivisorSigma[1, n]-1; Table[FixedPoint[f, n], {n, 2, 100}] (* T. D. Noe, May 10 2010 *) PROG (PARI) a(n)=local(m); if(n<2, 0, while((m=sigma(n)-1)!=n, n=m); n) \\ Franklin T. Adams-Watters, May 10 2010 (PARI) A039654(n)=n>1&&until(n==n=sigma(n)-1)!, ); n \\ M. F. Hasler, Sep 25 2017 CROSSREFS Cf. A039655 (the number of steps needed), A039649, A039650, A039651, A039652, A039653, A039656, A291301, A291302, A291776, A291777. For records see A292112, A292113. Cf. A177343: number of times the n-th prime occurs in this sequence. Cf. A292874: least k such that a(k) = prime(n). Sequence in context: A084743 A030391 A244496 * A075240 A347358 A333200 Adjacent sequences:  A039651 A039652 A039653 * A039655 A039656 A039657 KEYWORD nonn AUTHOR EXTENSIONS Contingency for no prime reached added by Franklin T. Adams-Watters, May 10 2010 Changed escape value from 0 to -1 to be consistent with several related sequences. - N. J. A. Sloane, Aug 31 2017 STATUS approved

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Last modified May 20 21:39 EDT 2022. Contains 353876 sequences. (Running on oeis4.)