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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A363295 Numbers k such that k and k+20 are consecutive unitary weird numbers (A064114).

Original entry on oeis.org

34121990, 34428290, 34766810, 34936070, 38014970, 38152010, 39506090, 39844610, 41400170, 42044990, 42552770, 42584990, 43769810, 46276490, 46308710, 47155010, 47324270, 47461310, 49016870, 49153910, 49323170, 49661690, 49863170, 50540210, 51015770, 51354290, 53079110
Offset: 1

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Author

Amiram Eldar, May 26 2023

Keywords

Comments

Conjecture: All the unitary weird numbers are of the form 20*k + 10, and thus 20 is the least gap between consecutive unitary weird numbers (verified for the 16326260 unitary weird numbers below 10^10).

Examples

			34121990 is a term since 34121990 = A064114(53235) and 34122010 = 34121990 + 20 = A064114(53236) are consecutive unitary weird numbers.
		

Crossrefs

A364975 Admirable numbers (A111592) with a record gap to the next admirable number.

Original entry on oeis.org

12, 30, 42, 88, 120, 140, 186, 534, 678, 6774, 7962, 77118, 94108, 152826, 478194, 662154, 935564, 1128174, 2028198, 6934398, 7750146, 8330924, 9984738, 10030804, 22956114, 62062566, 151040622, 284791602, 732988732, 804394974, 1151476732, 9040886574, 31302713634
Offset: 1

Views

Author

Amiram Eldar, Aug 15 2023

Keywords

Comments

The corresponding record gaps are 8, 10, 12, 14, 18, 34, 36, 48, 84, 132, 204, 216, 254, 312, 348, 360, 392, 468, 516, 528, 552, 598, 624, 638, 828, 852, 936, 1056, 1082, 1128, 1454, 1692, 1752, ... .

Examples

			The first 5 admirable numbers are 12, 20, 24, 30 and 40. The differences between these terms are 8, 4, 6 and 10. The record gaps, 8 and 10, occur after the terms 12 and 30, which are the first two terms of this sequence.
		

Crossrefs

Similar sequences: A306953, A330870, A334418, A334419, A334883, A363296.

Programs

  • Mathematica
    admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
    seq[kmax_] := Module[{s = {}, m = 12, dm = 0}, Do[If[admQ[k], d = k - m; If[d > dm, dm = d; AppendTo[s, m]]; m = k], {k, m + 1, kmax}]; s]; seq[10^6]
  • PARI
    isadm(n) = {my(ab=sigma(n)-2*n); ab>0 && ab%2 == 0 && ab/2 < n && n%(ab/2) == 0; }
    lista(kmax) = {my(m = 12, dm = 0); for(k = m+1, kmax, if(isadm(k), d = k - m; if(d > dm, dm = d; print1(m, ", ")); m = k));}
Showing 1-2 of 2 results.