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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A278441 Numbers n such that n | A244112(n).

Original entry on oeis.org

1, 2, 5, 10, 22, 26, 32, 62, 91, 330, 370, 519, 575, 710, 1060, 4055, 29377, 79554, 108690, 150320, 306440, 2510048, 3605570, 14233221, 14331231, 14333110, 14509410, 15143331, 15233221, 15331231, 15333110, 16143331, 16153331, 16233221, 16331231, 16333110, 17143331
Offset: 1

Views

Author

Paolo P. Lava, Nov 25 2016

Keywords

Comments

The sequence is bounded. See comment in A278439.

Examples

			A244112(519) = 191511 and 191511 / 519 = 369.

Links

Crossrefs

Cf. A237605, A244112, A278439, A278440.

Programs

  • Maple
    with(numtheory): P:=proc(q) local a,b,c,d,j,k,n; for n from 1 to q do a:=sort(convert(n,base,10));
for k from 1 to trunc(nops(a)/2) do c:=a[k]; a[k]:=a[nops(a)-k+1]; a[nops(a)-k+1]:=c; od;  k:=1; b:=a[1]; c:=0;
for j from 2 to nops(a) do if a[j]=b then k:=k+1; else d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; k:=1; b:=a[j]; fi; od;
d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; if type(c/n,integer) then print(n); fi; od; end: P(10^99);

A278439 Numbers k such that k | A047842(k).

Original entry on oeis.org

1, 2, 5, 22, 105, 188, 258, 327, 663, 15425, 16654, 27848, 40324, 80328, 481263, 10213223, 10311233, 10313314, 10313315, 10313316, 10313317, 10313318, 10313319, 21322314, 21322315, 21322316, 21322317, 21322318, 21322319, 31123314, 31123315, 31123316, 31123317
Offset: 1

Views

Author

Paolo P. Lava, Nov 22 2016

Keywords

Comments

The sequence is bounded. Let us consider a k-digit number n in which all 10 numerals from 0 to 9 are equally distributed: there are k/10 0's, k/10 1's, etc. This is the best case in order to have a number with the greatest number of digits under the transform n -> A047842(n). The number of digits we get is 10 + 10*floor(log_10(k/10) + 1), which must be >= k. The inequality becomes log_10(k/10) >= k/10 - 2, which is solved by k <= 23.75... This means that no term of the sequence can have more than 23 digits.

Examples

			A237605(258) = 121518 and 121518/258 = 471.

Links

Crossrefs

Cf. A047842, A237605, A278440, A278441.

Programs

  • Maple
    with(numtheory): P:=proc(q) local a,b,c,d,j,k,n; for n from 1 to q do
a:=sort(convert(n,base,10)); k:=1; b:=a[1]; c:=0; for j from 2 to nops(a) do
if a[j]=b then k:=k+1; else d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; k:=1; b:=a[j]; fi; od;
d:=10*k+b; c:=c*10^(ilog10(d)+1)+d; if type(c/n,integer) then print(n); fi; od; end: P(10^10);

Extensions

a(32) corrected by Sean A. Irvine, May 27 2025

A343455 Numbers where A244112(n) = n.

Original entry on oeis.org

22, 14233221, 14331231, 14333110, 15143331, 15233221, 15331231, 15333110, 16143331, 16153331, 16233221, 16331231, 16333110, 17143331, 17153331, 17163331, 17233221, 17331231, 17333110, 18143331, 18153331, 18163331, 18173331, 18233221, 18331231, 18333110, 19143331
Offset: 1

Views

Author

J. Lowell, Apr 15 2021

Keywords

Comments

Intersection of A278440 and A278441.
Fixed points of A244112.

Examples

			14233221 has one 4, two 3's, three 2's, and two 1's.

Links

Crossrefs

Cf. A244112, A278440, A278441.

Extensions

a(9) and beyond from Martin Ehrenstein, Apr 16 2021
Showing 1-3 of 3 results.

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