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A243058 Fixed points of A243057 and A243059. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A205523 A145739 A198191 * A288863 A121700 A080980

Adjacent sequences:  A243055 A243056 A243057 * A243059 A243060 A243061

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 31 2014

STATUS

approved

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Last modified January 23 01:55 EST 2018. Contains 298093 sequences.