A338452 Numbers k such that k and k+1 have the same total binary weight of their divisors (A093653).

3, 4, 7, 20, 31, 57, 94, 98, 118, 122, 127, 201, 213, 218, 230, 242, 243, 244, 334, 384, 393, 423, 429, 481, 565, 603, 633, 694, 704, 729, 766, 844, 921, 1138, 1141, 1221, 1262, 1401, 1533, 1654, 1726, 1761, 1837, 1838, 1862, 1882, 1942, 2162, 2245, 2361, 2362

Offset

1,1

Comments

Numbers k such that A093653(k) = A093653(k+1).

The Mersenne primes (A000668) are terms since if 2^p - 1 is a prime then A093653(2^p-1) = A093653(2^p) = p+1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

3 is a term since A093653(3) = A093653(4) = 3.

Mathematica

f[n_] := DivisorSum[n, DigitCount[#, 2, 1] &]; s = {}; f1 = f[1]; Do[f2 = f[n]; If[f1 == f2, AppendTo[s, n - 1]]; f1 = f2, {n, 2, 240}]; s

Crossrefs

Cf. A000120, A093653.

A000668 is a subsequence.

Similar sequences: A002961, A005237, A054004, A064125, A238380, A293183, A306985.

Sequence in context: A169892 A246805 A241660 * A030724 A124082 A056655

Adjacent sequences: A338449 A338450 A338451 * A338453 A338454 A338455

Keyword

nonn,base

Author

Amiram Eldar, Oct 28 2020

Status

approved