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

1,3

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

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A007814, A350877, A350616, A350618.

Sequence in context: A086632 A038699 A249803 * A064655 A207335 A049604

Adjacent sequences: A350830 A350831 A350832 * A350834 A350835 A350836

Keyword

nonn

Author

M. F. Hasler, Jan 23 2022

Status

approved