A110751 - OEIS

A110751

Numbers n such that n and its digital reversal have the same prime divisors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Contains the palindromes A002113 as a subsequence. 1089 and 2178 are the first two non-palindromic terms. Any number of concatenations of 1089 with itself or 2178 with itself gives a term; e.g. 10891089 etc. Hence there are infinitely many non-palindromic terms. They are given in A110819.

LINKS

Derek Orr, Table of n, a(n) for n = 1..1000

EXAMPLE

1089 = 3^2*11^2, 9801 = 3^4*11^2.

MATHEMATICA

Select[ Range[ 500], First /@ FactorInteger[ # ] == First /@ FactorInteger[ FromDigits[ Reverse[ IntegerDigits[ # ]]]] &] (* Robert G. Wilson v *)

PROG

(PARI) is_A110751(n)={ local(r=eval(concat(vecextract(Vec(Str(n)), "-1..1")))); r==n || factor(r)[, 1]==factor(n)[, 1] } /* M. F. Hasler */

(Python)

from sympy import primefactors

A110751 = [n for n in range(1, 10**5) if primefactors(n) == primefactors(int(str(n)[::-1]))] # Chai Wah Wu, Aug 14 2014

CROSSREFS