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

1,1

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.

Links

Table of n, a(n) for n=1..21.

Example

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

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

Crossrefs

Cf. A093653.

Subsequence of A338452, A338453 and A338454.

Similar sequences: A045933, A045941, A049051.

Sequence in context: A186909 A288089 A257901 * A202723 A230795 A172654

Adjacent sequences: A338452 A338453 A338454 * A338456 A338457 A338458

Keyword

nonn,base

Author

Amiram Eldar, Oct 28 2020

Status

approved