login
A293715
Numbers k such that A007755(k) is prime.
1
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
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
Sequence in context: A167904 A347769 A004841 * A276393 A193457 A161950
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 15 2017
STATUS
approved