A329225 a(n) is the smallest number k such that Sum_{i=1..k} Kronecker(prime(i),prime(n)) > 0 (or equivalently, Sum_{i=1..k} Kronecker(prime(i),prime(n)) = 1), or 0 if no such k exists.

732722, 23338590792, 102091236, 1, 3, 314, 1, 5, 1, 128, 1, 5, 1, 16, 1, 7, 3, 3, 38, 1, 1, 1, 5, 1, 1, 9, 1, 9, 3, 1, 1, 3, 1, 5, 11, 1, 7, 1760, 1, 15, 3, 3, 1, 1, 15, 1, 17, 1, 5, 3, 1, 1, 1, 3, 1, 1, 15, 1, 9, 1, 25, 70, 27, 1, 1, 19, 35, 1, 19, 3, 1, 1, 1, 7, 41, 1, 5

Offset: 1

Author

Jianing Song, Nov 08 2019

Keywords

• nonn

Comments

a(n) is the index in primes of A329224(n), or 0 if A329224(n) = 0.

For further information see A329224, which is the main entry for these sequences.

Examples

			For prime(10) = 29, k = 128 is the first case such that Sum_{i=1..k} Kronecker(prime(i),29) = 1 > 0, so a(10) = 128.
		

Crossrefs

Cf. A306502, A306503. See A329224 for the actual primes.

Programs

PARI

a(n) = if(n==2, 23338590792, if(n==3, 102091236, my(p=prime(n), i=0); forprime(q=2, oo, i+=kronecker(q, p); if(i>0, return(primepi(q))))))

Extensions

Edited by Peter Munn, Jun 26 2025