A147814 a(n) is the number of bits in the Elias omega-coded value of prime(n).

4, 4, 7, 7, 8, 8, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17

Offset

1,1

Comments

a(n) increases very slowly, gradually diverging from 3 + floor(log_2(n)).

Links

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Sean A. Irvine, Java program (github)

Wikipedia, Elias omega coding

Formula

a(n) = 2 + Sum_{i=0..k} d(i, prime(n)), where d(0, m) = bits(m) and d(i, m) = bits(d(i-1, m) - 1) and k is the least index such that d(k,prime(n))=2, and bits(m) = 1 + floor(log_2(m)) is the number of bits in the binary representation of m.

Crossrefs

Cf. A000040, A147764.

Sequence in context: A023404 A140245 A200364 * A168233 A238391 A049647

Adjacent sequences: A147811 A147812 A147813 * A147815 A147816 A147817

Keyword

base,easy,nonn

Author

Reikku Kulon, Nov 13 2008

Extensions

Edited by Sean A. Irvine, Mar 29 2026

Status

approved