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

Author

Antti Karttunen, May 31 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

A subsequence of A243068.

Apart from 1 also a subsequence of A102750.

A000040 is a subsequence.

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