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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A338455 Starts of runs of 5 consecutive numbers with the same total binary weight of their divisors (A093653).

Original entry on oeis.org

1307029927, 2116078861, 2665774183, 2809370965, 4108623302, 4493733751, 5333670902, 5497285284, 5679049670, 8209799382, 9665369455, 9708528486, 10353426151, 10606564910, 12777118615, 12795699493, 13660293367, 13847206214, 14351020663, 15735895813, 17912257013
Offset: 1

Views

Author

Amiram Eldar, Oct 28 2020

Keywords

Comments

Numbers k such that A093653(k) = A093653(k+1) = A093653(k+2) = A093653(k+3) = A093653(k+4).
Can 6 consecutive numbers have the same total binary weight of their divisors? If they exist, then they are larger than 10^11.

Examples

			1307029927 is a term since A093653(1307029927) = A093653(1307029928) = A093653(1307029929) = A093653(1307029930) = A093653(1307029931) = 72.
		

Crossrefs

Cf. A093653.
Subsequence of A338452, A338453 and A338454.
Similar sequences: A045933, A045941, A049051.

Programs

  • Mathematica
    f[n_] := DivisorSum[n, DigitCount[#, 2, 1] &]; s = {}; m = 5; fs = f /@ Range[m]; Do[If[Equal @@  fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^7}]; s

A338516 Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

Original entry on oeis.org

1377595575, 4275143301, 13616091683, 13640596128, 15016388244, 15176619135, 21361749754, 23605084359, 24794290167, 28025464183, 29639590888, 30739547718, 33924433023, 35259630279, 38008366692, 38670247670, 38681191672, 40210059079, 40507412213, 49759198333, 52555068607
Offset: 1

Views

Author

Amiram Eldar, Oct 31 2020

Keywords

Comments

Can 5 consecutive numbers be divisible by the total binary weight of their divisors? If they exist, then they are larger than 10^11.

Examples

			1377595575 is a term since the 4 consecutive numbers from 1377595575 to 1377595578 are all terms of A093705.
		

Crossrefs

Subsequence of A338514 and A338515.
Similar sequences: A141769, A330933, A334372, A338454.

Programs

  • Mathematica
    divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[4]; Reap[Do[If[And @@ div, Sow[k - 4]]; div = Join[Rest[div], {divQ[k]}], {k, 5, 5*10^9}]][[2, 1]]
    SequencePosition[Table[If[Mod[n,Total[Flatten[IntegerDigits[#,2]&/@Divisors[n]]]]==0,1,0],{n,526*10^8}],{1,1,1,1}][[;;,1]] (* The program will take a long time to run. *) (* Harvey P. Dale, May 28 2023 *)
Showing 1-2 of 2 results.