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A020485 Least positive palindromic multiple of n, or 0 if none exists. 6
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 (list; graph; refs; listen; history; text; internal format)
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)

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: A080434 A062567 A069554 * 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

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Last modified January 23 12:31 EST 2021. Contains 340385 sequences. (Running on oeis4.)