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.

Showing 1-5 of 5 results.

A259727 Sum of digits of a(n) equals the sum of digits of 3*a(n).

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 72, 81, 90, 99, 108, 117, 135, 144, 171, 180, 189, 198, 207, 234, 270, 279, 288, 297, 342, 351, 360, 396, 405, 414, 441, 450, 459, 486, 495, 504, 540, 549, 558, 576, 585, 594, 639, 648, 657, 693, 702, 711, 720, 729, 756, 765, 783, 792
Offset: 1

Views

Author

Christina Steffan, Jul 04 2015

Keywords

Comments

A007953(a(n)) = A007953(3*a(n)).
a(n) is a multiple of 9, but not all multiples of 9 belong to the sequence: e.g., 63 = 7*9: A007953(63) = 6 + 3 = 9, but A007953(3*63) = A007953(189) = 1 + 8 + 9 = 18.

Examples

			99 belongs to the sequence, because A007953(99) = 18 = A007953(297) = A007953(3*99).

Crossrefs

Cf. A007953, A070279, A259728, A259729.

Programs

  • Magma
    [n: n in [0..800] | &+Intseq(n) eq &+Intseq(3*n)]; // Vincenzo Librandi, Aug 05 2015
  • Mathematica
    Select[Range[0, 800], Total@ IntegerDigits@ # == Total@ IntegerDigits[3 #] &] (* Michael De Vlieger, Aug 05 2015 *)
  • PARI
    select(x->sumdigits(x)==sumdigits(3*x),vector(10^4,n,n)) \\ Joerg Arndt, Jul 04 2015

A259728 Sum of digits of a(n) equals the sum of digits of 4*a(n).

Original entry on oeis.org

0, 3, 6, 9, 15, 18, 27, 30, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 66, 69, 81, 84, 87, 90, 93, 96, 99, 105, 108, 126, 129, 135, 138, 150, 153, 156, 159, 165, 168, 177, 180, 183, 186, 189, 195, 198, 225, 228, 252, 261, 264, 267, 270, 273, 282, 291, 294, 297
Offset: 1

Views

Author

Christina Steffan, Jul 05 2015

Keywords

Comments

A007953(a(n)) = A007953(4*a(n)).
a(n) is a multiple of 3, but not all multiples of 3 belong to the sequence: e.g., 12 = 4*3: A007953(12) = 1 + 2 = 3, but A007953(4*12) = A007953(48) = 4 + 8 = 12.

Examples

			15 belongs to the sequence, because A007953(15) = 6 = A007953(60) = A007953(4*15).

Crossrefs

Cf. A007953, A070279, A259727, A259729.

Programs

  • Magma
    [n: n in [0..400] | &+Intseq(n) eq &+Intseq(4*n)]; // Vincenzo Librandi, Aug 05 2015

Extensions

More terms from Vincenzo Librandi, Aug 05 2015

A259729 Sum of digits of a(n) equals the sum of digits of 5*a(n).

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 126, 144, 162, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 297, 306, 324, 342, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 477, 495, 504, 522, 540, 549, 558, 567, 576, 585, 594
Offset: 1

Views

Author

Christina Steffan, Jul 05 2015

Keywords

Comments

A007953(a(n)) = A007953(5*a(n)).
a(n) is a multiple of 9, but not all multiples of 9 belong to the sequence: 117 = 13*9: A007953(117) = 1 + 1 + 7 = 9, but A007953(5*117) = A007953(585) = 5 + 8 + 5 = 18.

Examples

			18 belongs to the sequence, because A007953(18) = 9 = A007953(90) = A007953(5*18).

Crossrefs

Cf. A007953, A070279, A259727, A259728.

Programs

  • Magma
    [n: n in [0..800] | &+Intseq(n) eq &+Intseq(5*n)]; // Vincenzo Librandi, Aug 05 2015
  • Mathematica
    Select[Range[0, 600], Total@ IntegerDigits@ # == Total@ IntegerDigits[5 #] &] (* Michael De Vlieger, Aug 05 2015 *)

A276381 Numbers n such that there exist a number k with A007953(n) = A007953(k*n) and 1 < k < 10.

Original entry on oeis.org

3, 6, 9, 15, 18, 27, 30, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 105, 108, 117, 126, 129, 135, 138, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 207, 216, 219, 225, 228, 234, 243
Offset: 1

Views

Author

Altug Alkan, Sep 04 2016

Keywords

Comments

From Robert Israel, Dec 29 2020: (Start)
If n is a term, so are 10*n and (10^m+1)*n where 10^(m-1) > n.
All terms are divisible by 3. (End)

Examples

			15 is a term because A007953(15) = A007953(4*15).

Links

Crossrefs

Cf. A007953, A070279, A259727, A259728, A259729.

Programs

  • Maple
    filter:= proc(n) local t,k;
  t:= digsum(n);
  for k from 2 to 9 do if digsum(k*n)=t then return true fi od;
  false
end proc:
select(filter, [seq(i,i=3..1000,3)]); # Robert Israel, Dec 29 2020

A302599 Numbers k such that digit_sum(k) > digit_sum(2k).

Original entry on oeis.org

5, 6, 7, 8, 15, 16, 17, 25, 26, 35, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79, 80, 85, 86, 87, 88, 89, 95, 96, 97, 98, 105, 106, 107, 115, 116, 125, 150, 151, 152, 155, 156, 157, 158, 159, 160, 161, 165, 166
Offset: 1

Views

Author

David Consiglio, Jr., Apr 10 2018

Keywords

Comments

Conjecture: a(n) ~ 2n. - Charles R Greathouse IV, Apr 10 2018
If n is in the sequence then so is 10*n. - David A. Corneth, Apr 10 2018
a(10^9) = 2367976531. - Charles R Greathouse IV, Apr 11 2018

Examples

			17 is in this sequence because 1+7 > 3+4.

Links

Crossrefs

Cf. A004092, A007953, A070279.

Programs

  • Maple
    select(t -> convert(convert(2*t,base,10),`+`)Robert Israel, Apr 12 2018
  • Mathematica
    With[{s = Array[Total@ IntegerDigits@ # &, 332]}, Select[Range@ Floor[Length[s]/2], s[[#]] > s[[2 #]] &]] (* Michael De Vlieger, Apr 10 2018 *)
  • PARI
    is(n)=sumdigits(n)>sumdigits(2*n) \\ Charles R Greathouse IV, Apr 10 2018
  • Python
    print([y for y in range(10000) if sum([int(x) for x in str(y)]) > sum([int(z) for z in str(2*y)])])
Showing 1-5 of 5 results.

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

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