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

0,3

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.

Formula

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

Crossrefs

Cf. A002113, A050782.

Sequence in context: A062567 A069554 A347346 * A083116 A084044 A169930

Adjacent sequences: A020482 A020483 A020484 * A020486 A020487 A020488

Keyword

nonn,base

Author

David W. Wilson

Extensions

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

Status

approved