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 1-4 of 4 results.

A248040 Numbers n such that n*digsum(n) contains the same distinct digits as n.

Original entry on oeis.org

1, 10, 100, 109, 190, 208, 280, 307, 370, 406, 450, 460, 505, 550, 604, 640, 703, 730, 802, 820, 901, 910, 1000, 1009, 1018, 1027, 1036, 1045, 1054, 1063, 1072, 1081, 1090, 1108, 1168, 1180, 1207, 1270, 1286, 1306, 1360, 1405, 1450, 1504, 1540, 1603, 1630, 1702, 1720, 1726, 1801
Offset: 1

Views

Author

Derek Orr, Sep 30 2014

Keywords

Comments

10^k is a subsequence for k >= 0. Thus this sequence is infinite.

Links

Crossrefs

Cf. A007953 (sum of digits), A011557 (powers of 10).
Cf. A247888 (similar, with n + product of digits), A247887 (similar, with n + digsum).

Programs

  • Maple
    filter:= proc(n) local L,s,d;
  L:= convert(n,base,10);
  d:= convert(L,set);
  s:= convert(L,`+`);
  evalb(convert(convert(n*s,base,10),set)=d)
end proc:
select(filter, [$1..2000]); # Robert Israel, Mar 06 2018
  • PARI
    for(n=1,10^4,d=digits(n);if(vecsort(d,,8)==vecsort(digits(n*sumdigits(n)),,8),print1(n,", ")))

A248209 Numbers n such that n - A007953(n) contains the same distinct digits as n.

Original entry on oeis.org

54, 243, 297, 432, 486, 621, 675, 810, 864, 1018, 1143, 1197, 1225, 1332, 1386, 1410, 1443, 1521, 1522, 1525, 1571, 1575, 1577, 1710, 1764, 1775, 1810, 1908, 1918, 1953, 1997, 2043, 2097, 2125, 2232, 2233, 2286, 2321, 2332, 2333, 2421, 2475, 2521, 2610
Offset: 1

Views

Author

Derek Orr, Oct 03 2014

Keywords

Crossrefs

Cf. A247887 (similar, with n + A007953(n)).

Programs

  • Magma
    [n: n in [1..3000] | Set(Intseq(n-&+Intseq(n))) eq Set(Intseq(n))]; // Bruno Berselli, Oct 12 2014
  • PARI
    for(n=1, 10^4, d=digits(n); if(vecsort(digits(n), , 8)==vecsort(digits(n-sumdigits(n)), , 8), print1(n, ", ")))
  • PARI
    is(n)=Set(digits(n))==Set(digits(n-sumdigits(n))) \\ Charles R Greathouse IV, Oct 12 2014

Formula

a(n) ~ n. More specifically, a(n) - n = O(n^k * log n) with k = log 9/log 10. (This bound is not tight.) - Charles R Greathouse IV, Oct 12 2014

A248039 Numbers n such that n*A007954(n) contains the same distinct digits as n.

Original entry on oeis.org

0, 1, 11, 111, 792, 1111, 1376, 2174, 2841, 11111, 11628, 12168, 12763, 12841, 14213, 14228, 14663, 19842, 24314, 24679, 24738, 24786, 26439, 26731, 26938, 29126, 39117, 39228, 49326, 64113, 76983, 79328, 83694, 83712, 83764, 86429, 87164, 89174, 92387, 92476, 93711, 94831, 98174
Offset: 1

Views

Author

Derek Orr, Sep 30 2014

Keywords

Comments

A002275 is a subsequence, thus this sequence is infinite.

Crossrefs

Cf. A002275 (repunits), A007954 (digit product).
Cf. A247887 (similar, with n + digit sum), A247888 (similar, with n + digit product).

Programs

  • Magma
    [n: n in [0..10^5] | Set(Intseq(n*&*Intseq(n))) eq Set(Intseq(n))]; // Bruno Berselli, Oct 09 2014
  • PARI
    for(n=0, 10^6, d=digits(n); p=prod(i=1, #d, d[i]); if(vecsort(digits(n), , 8)==vecsort(digits(n*p), , 8), print1(n, ", ")))

A248718 Numbers n such that n + (sum of digits of n) and n + (product of digits of n) contain the same distinct digits of n.

Original entry on oeis.org

1512, 4346, 5112, 5769, 11215, 11512, 12115, 12313, 12511, 13213, 14346, 14512, 15112, 15211, 15412, 21115, 21313, 21511, 23113, 25111, 27369, 31213, 32113, 34135, 34535, 41346, 41512, 43135, 43535, 45112, 51112, 51211, 51412, 52111, 52569, 53435, 53534, 53958, 54112, 54533, 56925
Offset: 1

Views

Author

Derek Orr, Oct 12 2014

Keywords

Comments

Intersection of A247887 and A247888.

Crossrefs

Cf. A247887, A247888, A007954, A007953, A052382.

Programs

  • PARI
    for(n=0,10^6,d=digits(n);p=prod(i=1,#d,d[i]);vp=vecsort(digits(p+n), ,8);vs=vecsort(digits(sumdigits(n)+n), ,8);if(vs==vp&&vp==vecsort(d, ,8)&&vs==vecsort(d, ,8)&&p,print1(n,", ")))
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.