A242423 Numbers in whose prime factorization the indices of primes do not sum to a triangular number.

3, 4, 7, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 23, 24, 26, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100

Offset

1,1

Comments

Numbers k such that A010054(A056239(k)) is zero, or equally, such that A002262(A056239(k)) is not zero.

These are numbers such that any iterations of A242424 started from them lead eventually to a cycle greater than one. Please see the comments and references at A242422.

Links

Antti Karttunen, Table of n, a(n) for n = 1..27575

Example

3 = p_2 is present, because 2 is not a triangular number.
4 = p_1 * p_1 is present, because 1+1 = 2 is not a triangular number.

Prog

(Scheme, with Antti Karttunen's Intseq-library)
(define A242423 (ZERO-POS 1 1 (COMPOSE A010054 A056239)))

Crossrefs

Complement: A242422.

Cf. A215366, A242424, A000217, A002262, A010054, A056239.

Sequence in context: A138225 A114889 A174659 * A010444 A010398 A010435

Adjacent sequences: A242420 A242421 A242422 * A242424 A242425 A242426

Keyword

nonn

Author

Antti Karttunen, May 16 2014

Status

approved