Voozh

A347297

a(1) = 1; for n >= 1, if a(n) is even then a(n+1) = a(n) / 2, otherwise, say a(n) is the k-th odd term in the sequence, a(n+1) = a(n) + k.

1, 2, 1, 3, 6, 3, 7, 12, 6, 3, 9, 16, 8, 4, 2, 1, 9, 18, 9, 19, 30, 15, 27, 40, 20, 10, 5, 19, 34, 17, 33, 50, 25, 43, 62, 31, 51, 72, 36, 18, 9, 31, 54, 27, 51, 76, 38, 19, 45, 72, 36, 18, 9, 37, 66, 33, 63, 94, 47, 79, 112, 56, 28, 14, 7, 41, 76, 38, 19, 55

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence is a variant of A350877; here we add positive integers, there prime numbers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Annotated log-log scatterplot of a(n), n = 1..2^16, showing records in red, labeling the indices of 1's in blue, appearances of powers of 2 in gold, and terms instigated by even predecessors in green.

EXAMPLE

a(1) = 1.

a(2) = a(1) + 1 = 2 as a(1) is the 1st odd term in the sequence.

a(3) = a(2) / 2 = 1 as a(2) is even.

a(4) = a(3) + 2 = 3 as a(3) is the 2nd odd term in the sequence.

a(5) = a(4) + 3 = 6 as a(4) is the 3rd odd term in the sequence.

MATHEMATICA

j = q = 1; {j}~Join~Reap[Do[If[EvenQ[j], k = j/2, k = j + q; q++]; Sow[k]; j = k, {i, 69}]][[-1, -1]] (* Michael De Vlieger, Jan 24 2022 *)

PROG

(PARI) print1 (v=1); for (k=1, 36, print1 (", "v+=k); while (v%2==0, print1 (", "v/=2)))

CROSSREFS

Cf. A347296, A350877.