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

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

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

Table of n, a(n) for n=1..62.

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