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

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

Offset: 1

Author

Amiram Eldar, Oct 28 2020

Keywords

• nonn
• base

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