A243058 Fixed points of A243057 and A243059.

1, 2, 3, 5, 6, 7, 11, 12, 13, 17, 19, 21, 23, 24, 29, 30, 31, 37, 41, 43, 47, 48, 53, 59, 61, 63, 65, 67, 70, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 113, 127, 131, 133, 137, 139, 149, 151, 154, 157, 163, 165, 167, 173, 179, 180, 181, 189, 191, 192, 193, 197, 199, 210

Offset

1,2

Comments

Number n is present if its prime factorization n = p_a * p_b * p_c * ... * p_i * p_j * p_k (where a <= b <= c <= ... <= i <= j <= k are the indices of prime factors, not necessarily all distinct; sorted into nondescending order) satisfies the condition that the first differences of those prime indices (a-0, b-a, c-b, ..., j-i, k-j) form a palindrome.

The above condition implies that none of the terms of A070003 are present, as then at least the difference k-j would be zero, but on the other hand, a-0 is at least 1. Cf. also A243068.

Links

Antti Karttunen, Table of n, a(n) for n = 1..2048

Example

12 = 2*2*3 = p_1 * p_1 * p_2 is present, as the first differences (deltas) of the indices of its nondistinct prime factors (1-0, 1-1, 2-1) = (1,0,1) form a palindrome.
18 = 2*3*3 = p_1 * p_2 * p_2 is NOT present, as the deltas of the indices of its nondistinct prime factors (1-0, 2-1, 2-2) = (1,1,0) do NOT form a palindrome.
65 = 5*13 = p_3 * p_6 is present, as the deltas of the indices of its nondistinct prime factors (3-0, 6-3) = (3,3) form a palindrome.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A243058 (FIXED-POINTS 1 1 A243057))

Crossrefs

A subsequence of A243068.

Apart from 1 also a subsequence of A102750.

A000040 is a subsequence.

Cf. A242413, A242417, A243057, A243059, A242417.

Sequence in context: A343027 A145739 A198191 * A348440 A339267 A288863

Adjacent sequences: A243055 A243056 A243057 * A243059 A243060 A243061

Keyword

nonn

Author

Antti Karttunen, May 31 2014

Status

approved