A242414 - OEIS

%I #15 May 31 2014 00:50:48

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29,30,31,

%T 32,33,34,35,36,37,38,39,41,42,43,46,47,49,51,53,55,57,58,59,61,62,64,

%U 65,66,67,69,70,71,73,74,77,78,79,81,82,83,85,86,87,89,90,91,93,94,95,97,100

%N Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic.

%C The fixed points of permutation A069799.

%C Differs from its subsequence, A072774, Powers of squarefree numbers, for the first time at n=68, as here a(68) = 90 is included, as 90 = p_1^1 * p_2^2 * p_3^1 has a palindromic tuple of exponents, even although not all of them are identical.

%C Differs from its another subsequence, A236510, in that, although numbers like 42 = 2^1 * 3^1 * 5^0 * 7^1, with a non-palindromic exponent-tuple (1,1,0,1) are excluded from A236510, it is included in this sequence, because here only the nonzero exponents are considered, and (1,1,1) is a palindrome.

%C Differs from A085924 in that as that sequence is subtly base-dependent, it excludes 1024 (= 2^10), as then the only exponent present, 10, and thus also its concatenation, "10", is not a palindrome when viewed in decimal base. On the contrary, here a(691) = 1024.

%H Antti Karttunen, <a href="/A242414/b242414.txt">Table of n, a(n) for n = 1..10000</a>

%e As 1 has an empty factorization, (), which also is a palindrome, 1 is present.

%e As 42 = 2 * 3 * 7 = p_1^1 * p_2^1 * p_4^1, and (1,1,1) is palindrome, 42 is present.

%e As 90 = 2 * 9 * 5 = p_1^1 * p_2^2 * p_3^1, and (1,2,1) is palindrome, 90 is present.

%e Any prime power (A000961) is present, as such numbers have a factorization p^e (e >= 1), and any singleton sequence (e) by itself forms a palindrome.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A242414 (FIXED-POINTS 1 1 A069799))

%Y Fixed points of A069799.

%Y Complement: A242416.

%Y A000961, A072774 and A236510 are subsequences.

%Y Cf. A242418, A085924.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 30 2014