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 A293715 Numbers k such that A007755(k) is prime. 0
 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 16, 18, 19, 21, 23, 24, 27, 28, 31, 33, 43, 51, 53, 54, 57, 60, 61, 62, 65, 67, 68, 69, 71, 73, 76, 79, 81, 83, 84, 89, 91, 110, 111, 115, 116, 118, 121, 124, 126, 129, 131, 132, 138, 139, 144, 145, 147, 149, 150, 153, 156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Shapiro conjectured that A007755(n) is prime for all n > 1, and verified it up to n = 10. Mills showed that A007755(34)=(2^16+1)^2 is composite. The least number n such that Omega(A007755(n)) = 1, 2, 3, ... is 2, 13, 30, 58, 74, 90, 106, 122, 146, 162, 178, 194, 210, 226, ... (Omega is the number of prime factors with multiplicity, A001222). REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, B41, p. 148. LINKS W. H. Mills, Iteration of the phi function, The American Mathematical Monthly, Vol. 50.9 (1943), pp. 547-549. Harold Shapiro, An arithmetic function arising from the phi function, The American Mathematical Monthly, Vol. 50, No. 1 (1943), pp. 18-30. EXAMPLE The first 11 values of A007755(n) after n=1 are the primes: 2, 3, 5, 11, 17, 41, 83, 137, 257, 641, 1097, 2329, therefore 2-12 are in the sequence. MATHEMATICA s = Import[b007755.txt", "Data"][[All, 2]]; a = Flatten[Position[s, _?(PrimeQ[#] &)]] (* using the b-File from A007755 *) CROSSREFS Cf. A007755, A092873. Sequence in context: A167904 A347769 A004841 * A276393 A193457 A161950 Adjacent sequences:  A293712 A293713 A293714 * A293716 A293717 A293718 KEYWORD nonn AUTHOR Amiram Eldar, Oct 15 2017 STATUS approved

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Last modified September 16 11:12 EDT 2021. Contains 347472 sequences. (Running on oeis4.)