A302031 An omega (A001221) analog based on the Ludic sieve (A255127): a(1) = 0; for n > 1, a(n) = 1 + a(A302034(n)).

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2

Offset: 1

Author

Antti Karttunen, Apr 02 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences generated by sieves

Crossrefs

Cf. A001221, A302026, A302037, A302041,

Cf. A302036 (positions of terms < 2).

Differs from similar A302041 for the first time at n=59, where a(59) = 2, while A302041(59) = 1.

Programs

PARI

\\ Assuming that A269379 and A269380 have been precomputed:
A302034(n) = if(1==n,n,my(k=0); while((n%2), n = A269380(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A269379(n); k--); (n));
A302031(n) = if(1==n,0,1+A302031(A302034(n)));

Formula

a(1) = 0; for n > 1, a(n) = 1 + a(A302034(n)).

a(n) = A001221(A302026(n)).

a(n) = A069010(A269388(n)).