cp's OEIS Frontend

A243058 Fixed points of A243057 and A243059.

%I A243058 #14 Jun 21 2014 14:15:31
%S A243058 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,
%T A243058 63,65,67,70,71,73,79,83,89,96,97,101,103,107,109,113,127,131,133,137,
%U A243058 139,149,151,154,157,163,165,167,173,179,180,181,189,191,192,193,197,199,210
%N A243058 Fixed points of A243057 and A243059.
%C A243058 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.
%C A243058 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.
%H A243058 Antti Karttunen, <a href="/A243058/b243058.txt">Table of n, a(n) for n = 1..2048</a>
%e A243058 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.
%e A243058 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.
%e A243058 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.
%o A243058 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A243058 (define A243058 (FIXED-POINTS 1 1 A243057))
%Y A243058 A subsequence of A243068.
%Y A243058 Apart from 1 also a subsequence of A102750.
%Y A243058 A000040 is a subsequence.
%Y A243058 Cf. A242413, A242417, A243057, A243059, A242417.
%K A243058 nonn
%O A243058 1,2
%A A243058 _Antti Karttunen_, May 31 2014