A129783 Conjectured numbers n with the property that there exist two consecutive primes p and q such that pq + n is a square.

1, 3, 4, 9, 10, 14, 16, 19, 21, 23, 25, 26, 29, 30, 34, 35, 36, 38, 43, 44, 46, 47, 49, 53, 58, 62, 64, 65, 66, 67, 68, 75, 77, 78, 81, 82, 83, 85, 86, 92, 94, 95, 100, 103, 106, 109, 110, 113, 115, 117, 118, 119, 121, 122, 125, 129, 134, 138, 139, 140, 143, 144, 146, 148

Offset: 1

Author

Cino Hilliard, May 18 2007

Keywords

• easy
• nonn
• obsc

Comments

Complement of A129816. [From Omar E. Pol, Dec 26 2008]

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029707, A074927.

Cf. A129816. [From Omar E. Pol, Dec 26 2008]

Programs

PARI

primesq(n,m) = \square of the form prime(x)*prime(x+1) + k {local(c,k,x,p1,p2,j); c=0; for(k=1,m, for(x=1,n, p1=prime(x); p2=(prime(x+1)); y=p1*p2+k; if(issquare(y), c++; print1(k","); break; ) ) ); c; }

Extensions

I don't know how many of the missing terms have been proved to be missing. Has it been proved that 2 is missing? - N. J. A. Sloane, May 20 2007