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

Offset: 1

Author

Amarnath Murthy, Aug 11 2005

Keywords

• base
• easy
• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A002113, A110819.

Programs

Mathematica

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

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

Extensions

Edited and extended by Robert G. Wilson v, Sep 21 2005

Corrected comment, added PARI code. - M. F. Hasler, Nov 16 2008