A350833 Run lengths of even terms in A350877 (half if even, add next prime if odd).

0, 1, 3, 3, 2, 4, 1, 2, 1, 2, 1, 1, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 2, 1, 5, 1, 2, 1, 1, 2, 1, 2, 6, 1, 2, 1, 2, 2, 5, 2, 5, 2, 1, 3, 2, 1, 2, 2, 4, 3, 3, 4, 1, 2, 5, 1, 1, 1, 1, 1, 3, 1, 3, 2, 1, 3, 2, 2, 3, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 2, 4, 3, 3, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2

Offset: 1

Author

M. F. Hasler, Jan 23 2022

Keywords

• nonn

Comments

Equals first differences of indices of odd terms (A350616) minus one.

After the initial 0, also equals the 2-valuation (A007814) of A350618, the terms following odd terms in A350877.

Record values are a(1) = 0, a(2) = 1, a(3) = 3, a(6) = 4, a(16) = 5, a(33) = 6, a(146) = 7, a(243) = 11, a(1596) = 12, a(2092) = 13, ... The first occurrences of the other values are: a(5) = 2, a(8) = 510, a(9) = 667, a(10) = 1526. No others up to n = 33000. - M. F. Hasler, Jan 24 2022

Examples

			Between the first odd term, A350877(1) = 1, and second odd term, A350877(2) = 3, there are no even terms, therefore a(1) = 0.
Between the second and third odd term, A350877(4) = 3, there is one even term, A350877(3) = 6, therefore a(2) = 1.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A350877, A350616, A350618.

Programs

PARI

A350833_upto(N)={N=A350616_upto(N);[N[k]-N[k-1]-1|k<-[2..#N]]}

Formula

a(n) = A350616(n+1) - A350616(n) - 1 = A007814(A350618(n-1)) for n > 1.