cp's OEIS Frontend

A293715 Numbers k such that A007755(k) is prime.

%I A293715 #14 Oct 09 2024 06:38:09
%S A293715 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,
%T A293715 57,60,61,62,65,67,68,69,71,73,76,79,81,83,84,89,91,110,111,115,116,
%U A293715 118,121,124,126,129,131,132,138,139,144,145,147,149,150,153,156
%N A293715 Numbers k such that A007755(k) is prime.
%C A293715 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.
%C A293715 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).
%D A293715 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, B41, p. 148.
%H A293715 Amiram Eldar, <a href="/A293715/b293715.txt">Table of n, a(n) for n = 1..289</a>
%H A293715 W. H. Mills, <a href="http://www.jstor.org/stable/2303426">Iteration of the phi function</a>, The American Mathematical Monthly, Vol. 50.9 (1943), pp. 547-549.
%H A293715 Harold Shapiro, <a href="http://www.jstor.org/stable/2303988">An arithmetic function arising from the phi function</a>, The American Mathematical Monthly, Vol. 50, No. 1 (1943), pp. 18-30.
%e A293715 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.
%t A293715 s = Import[b007755.txt", "Data"][[All, 2]]; a = Flatten[Position[s, _?(PrimeQ[#] &)]] (* using the b-File from A007755 *)
%Y A293715 Cf. A007755, A092873.
%K A293715 nonn
%O A293715 1,1
%A A293715 _Amiram Eldar_, Oct 15 2017