The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242414 Numbers whose prime factorization viewed as a tuple of nonzero powers is palindromic. 24
 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, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The fixed points of permutation A069799. 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. 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. 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 EXAMPLE As 1 has an empty factorization, (), which also is a palindrome, 1 is present. As 42 = 2 * 3 * 7 = p_1^1 * p_2^1 * p_4^1, and (1,1,1) is palindrome, 42 is present. As 90 = 2 * 9 * 5 = p_1^1 * p_2^2 * p_3^1, and (1,2,1) is palindrome, 90 is present. 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. PROG (Scheme, with Antti Karttunen's IntSeq-library) (define A242414 (FIXED-POINTS 1 1 A069799)) CROSSREFS Fixed points of A069799. Complement: A242416. A000961, A072774 and A236510 are subsequences. Cf. A242418, A085924. Sequence in context: A304449 A360247 A085924 * A072774 A062770 A359889 Adjacent sequences: A242411 A242412 A242413 * A242415 A242416 A242417 KEYWORD nonn AUTHOR Antti Karttunen, May 30 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 8 20:00 EST 2023. Contains 360152 sequences. (Running on oeis4.)