A020485 Least positive palindromic multiple of n, or 0 if none exists.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 252, 494, 252, 525, 272, 272, 252, 171, 0, 252, 22, 161, 696, 525, 494, 999, 252, 232, 0, 434, 2112, 33, 272, 525, 252, 111, 494, 585, 0, 656, 252, 989, 44, 585, 414, 141, 2112, 343, 0, 969, 676, 212, 27972, 55, 616, 171, 232, 767, 0, 26962

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base

Comments

Smallest positive palindrome divisible by n, or 0 if no such palindrome exists (which happens iff n is a multiple of 10). - N. J. A. Sloane, Apr 04 2019

The existence of palindromic multiples is a corollary of the theorem that an arithmetic progression with initial term c and a positive common difference d contains infinitely many palindromic numbers unless both of these numbers are multiples of 10. - M. Harminc (harminc(AT)duro.science.upjs.sk), Jul 14 2000

Links

• Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 8181 terms from N. J. A. Sloane)
• Ely Golden, Python program for generating terms of this sequence
• M. Harminc and R. Sotak, Palindromic numbers in arithmetic progressions, Fibonacci Quarterly Journal, Jun-Jul (1998), pp. 259-262.

Crossrefs

Cf. A002113, A050782.

Formula

a(n) = n*A050782(n). - Michel Marcus, Jan 22 2019

Extensions

a(0)=0 added by N. J. A. Sloane, Apr 04 2019