A347296 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) + a(k).

1, 2, 1, 3, 4, 2, 1, 4, 2, 1, 5, 7, 8, 4, 2, 1, 5, 7, 8, 4, 2, 1, 6, 3, 10, 5, 13, 17, 19, 20, 10, 5, 10, 5, 12, 6, 3, 11, 15, 17, 18, 9, 15, 18, 9, 19, 24, 12, 6, 3, 16, 8, 4, 2, 1, 18, 9, 28, 14, 7, 27, 37, 42, 21, 31, 36, 18, 9, 21, 27, 30, 15, 26, 13, 28

Offset: 1

Author

Rémy Sigrist, Jan 23 2022

Keywords

• nonn

Comments

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

Examples

			a(1) = 1.
a(2) = a(1) + a(1) = 2 as a(1) is the 1st odd term.
a(3) = a(2) / 2 = 1 as a(2) is even.
a(4) = a(3) + a(2) = 3 as a(3) is the 2nd odd term.
a(5) = a(4) + a(3) = 4 as a(4) is the 3rd odd term.
		

Links

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

Crossrefs

Cf. A347297, A350877.

Programs

PARI

k=0; for (n=1, #a=vector(75), print1 (a[n]=if (n==1, 1, a[n-1]%2==0, a[n-1]/2, a[n-1]+a[k++])", "))