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A332063 a(1) = 1, a(n + 1) = a(n) + Sum_{k = 1..n} floor(log_2(a(k)) + 1): add total number of bits of the terms so far. 1
1, 2, 5, 11, 21, 36, 57, 84, 118, 159, 208, 265, 331, 406, 490, 583, 686, 799, 922, 1055, 1199, 1354, 1520, 1697, 1885, 2084, 2295, 2518, 2753, 3000, 3259, 3530, 3813, 4108, 4416, 4737, 5071, 5418, 5778, 6151, 6537, 6936, 7348, 7773, 8211, 8663, 9129, 9609, 10103, 10611 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

By number of bits we mean A070939 (length of base-2 representation), not the sum of nonzero bits or Hamming weight A000120.

One might consider starting this sequence with a(0) = 0, and defining (for the purpose of this sequence) log 0 = 0 as to get 1 for the number of bits of zero (although it is as well justified to consider 0 to have 0 bits). In that case one would get the sequence b(n) = a(n) + (n-1): (0, 1, 3, 7, 14, 25, 41, 63, 91, 126, 168, ...), similar to, but different from A004006.

LINKS

Table of n, a(n) for n=1..50.

PROG

(PARI) ({A332063_vec(N, a=1, s=-a)=vector(N, n, a+=s+=exponent(a)+1)})(50)

CROSSREFS

Cf. A070939 (length of base-2 representation), A000120 (hammingweight).

Cf. A332064 for a variant where the number of bits is added or subtracted, depending on the parity of a(n).

Sequence in context: A005575 A328670 A294745 * A050407 A113032 A100134

Adjacent sequences:  A332060 A332061 A332062 * A332064 A332065 A332067

KEYWORD

nonn

AUTHOR

M. F. Hasler, Feb 26 2020

STATUS

approved

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Last modified July 10 12:34 EDT 2020. Contains 335576 sequences. (Running on oeis4.)