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 1-3 of 3 results.

A067869 Numbers n such that n and 2^n end with the same 5 digits.

Original entry on oeis.org

48736, 148736, 248736, 348736, 448736, 548736, 648736, 748736, 848736, 948736, 1048736, 1148736, 1248736, 1348736, 1448736, 1548736, 1648736, 1748736, 1848736, 1948736, 2048736, 2148736, 2248736, 2348736, 2448736, 2548736
Offset: 1

Views

Author

Benoit Cloitre, Mar 07 2002

Keywords

Links

Crossrefs

Cf. A064541.
Subsequence of A067844, A067845, A067846, and A067847.

Programs

  • PARI
    isok(n) = (2^n - n) % 100000 == 0; \\ Michel Marcus, Nov 23 2013

Formula

a(n) = 48736+10^5(n-1).
a(n) = 2*a(n-1)-a(n-2). G.f.: x*(48736+51264*x)/(1-x)^2. - Colin Barker, Jun 05 2012

A341119 a(n) is the least positive number that has exactly n divisors d such that d-1 is prime.

Original entry on oeis.org

1, 3, 6, 18, 12, 36, 24, 48, 72, 120, 168, 336, 240, 540, 360, 960, 840, 1080, 720, 1680, 3024, 1440, 2160, 2880, 2520, 6480, 4320, 14040, 8640, 5040, 9240, 7560, 23520, 12600, 18480, 10080, 33600, 22680, 15120, 20160, 36960, 27720, 47880, 40320, 37800, 47520, 30240, 80640, 85680, 65520, 60480
Offset: 0

Views

Author

J. M. Bergot and Robert Israel, Feb 05 2021

Keywords

Comments

a(n) is the least positive solution to A072627(k) = n.
The conjectured terms are exact if for 0 <= n <= 10000 we have a(n) / A046523(A000005(a(n))) <= 9. For the found terms, a(n) / A046523(A000005(a(n))) <= 7.3. - David A. Corneth, Jun 15 2022

Examples

			a(3) = 18 has 3 such divisors: 2+1=3, 5+1=6, 17+1=18, and is the least number with exactly 3.

Links

Crossrefs

Cf. A000005, A008864, A046523, A067846, A072627, A341099.

Programs

  • Maple
    f:= proc(n) nops(select(t -> isprime(t-1), numtheory:-divisors(n))) end proc:
N:= 60: count:= 0:
V:= Array(0..N):
for n from 1 while count < N+1 do
  v:= f(n);
  if v <= N and V[v] = 0 then
    count:=count+1;
    V[v]:= n;
  fi;
od:
convert(V,list);
  • Mathematica
    With[{s = Array[DivisorSum[#, 1 &, PrimeQ[# - 1] &] &, 10^5]}, Array[FirstPosition[s, #][[1]] &, 51, 0]] (* Michael De Vlieger, Feb 05 2021 *)
  • PARI
    a(n) = my(k=1); while (sumdiv(k, d, isprime(d-1)) != n, k++); k; \\ Michel Marcus, Feb 05 2021

A067867 Numbers n such that n and 2^n end with the same 4 digits.

Original entry on oeis.org

8736, 18736, 28736, 38736, 48736, 58736, 68736, 78736, 88736, 98736, 108736, 118736, 128736, 138736, 148736, 158736, 168736, 178736, 188736, 198736, 208736, 218736, 228736, 238736, 248736, 258736, 268736, 278736, 288736, 298736, 308736
Offset: 1

Views

Author

Benoit Cloitre, Mar 07 2002

Keywords

Links

Crossrefs

Cf. A064541.
Subsequence of A067844, A067845 and A067846.

Programs

  • PARI
    isok(n) = (2^n - n) % 10000 == 0; \\ Michel Marcus, Nov 23 2013

Formula

a(n) = 8736 + 10^4(n-1).
a(n) = 2*a(n-1)-a(n-2). G.f.: 16*x*(546+79*x)/(1-x)^2. [Colin Barker, Dec 01 2012]
Showing 1-3 of 3 results.

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

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