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A338455 Starts of runs of 5 consecutive numbers with the same total binary weight of their divisors (A093653). 0
1307029927, 2116078861, 2665774183, 2809370965, 4108623302, 4493733751, 5333670902, 5497285284, 5679049670, 8209799382, 9665369455, 9708528486, 10353426151, 10606564910, 12777118615, 12795699493, 13660293367, 13847206214, 14351020663, 15735895813, 17912257013 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 15:14 EST 2021. Contains 349526 sequences. (Running on oeis4.)