A160218 Index at which n-th prime occurs in A160256, or -1 if the prime never occurs.

2, 3, 14, 20, 32, 301, 1065

Offset: 1

Author

M. F. Hasler, May 06 2009

Keywords

• hard
• more
• nonn

Comments

A160256(a(n))=A000040(n) if and only if both Conjectures 1 and 2 are true:

Conjecture 1: Primes occur in A160256 in increasing order.

Conjecture 2: All primes occur in A160256.

Conjecture 3: Except for A160256(4)=4, the least positive integer which does not occur in A160256 up to a given index is always a prime (and thus of the form A160256(a(k)) for some k).

Conjecture 4: A160256(a(n)) is always the least positive integer which did not occur earlier in A160256.

Crossrefs

Cf. A160256, A151413.

Programs

PARI

list_A160218(n)={ my(a1=1,a2=1,S=[]); until( isprime(a1) & !print1(#S,",") & !n--, for( a=1,9e9, a*a1%a2 & next; setsearch(S,a) & next; a2=a1; S=setunion(S,Set(a1=a)); /*print1(a",");*/ next(2)); error);vecsort(eval(S)) }

Extensions

Edited by N. J. A. Sloane, May 16 2009