cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A008593 Multiples of 11.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Numbers for which the sum of "digits" in base 100 is divisible by 11. For instance, 193517302 gives 1 + 93 + 51 + 73 + 02 = 220, and 2 + 20 = 22 = 2 * 11. - Daniel Forgues, Feb 22 2016
Numbers in which the sum of the digits in the even positions equals the sum of the digits in the odd positions. - Stefano Spezia, Jan 05 2025

Links

Crossrefs

Cf. A008591, A008592, A008604, A059632; union of A135499 and A060979.

Programs

Formula

a(n) = 11*n.
G.f.: 11*x/(1-x)^2. - David Wilding, Jun 21 2014
E.g.f.: 11*x*exp(x). - Stefano Spezia, Oct 08 2022
From Elmo R. Oliveira, Apr 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2).
a(n) = A008604(n)/2. (End)

A039691 If n=x1x2...xm in base 10, n belongs to the sequence iff x1x2..xm*11=y1y2...ym and xm..x2x1*11=ym...y2y1.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110
Offset: 1

Views

Author

Felice Russo

Keywords

Comments

This pattern works whenever the adjacent digits of a number do not add to more than 9.
A059632(a(n)) = 11*a(n). - Reinhard Zumkeller, Jul 05 2014

Examples

			45*11=495 and 54*11=594, so 45 is a term.

References

  • D. Wells, Curious and interesting numbers, Penguin Books, p. 156

Links

Crossrefs

Cf. A003714, A242407.

Programs

  • Haskell
    a039691 n = a039691_list !! (n-1)
a039691_list = filter (f 0) [0..] where
   f d x = d' + d < 10 && (x < 10 || f d' x') where (x', d') = divMod x 10
-- Reinhard Zumkeller, Jul 05 2014
  • PARI
    isok(n) = my(d = digits(n), y = n*11); fromdigits(Vecrev(digits(y))) == fromdigits(Vecrev(d))*11; \\ Michel Marcus, Sep 05 2017

Extensions

Offset corrected by Reinhard Zumkeller, Jul 05 2014
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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