A081640 a(n) = n-th prime of class 12- according to the Erdős-Selfridge classification.

14920303, 18224639, 24867247, 26532953, 34548443, 38003011, 39800743, 41319599, 41443483, 45604771, 46432667, 47247763, 49734341, 49734493, 49749439, 51591833, 53014667, 55257977, 59681383, 59700749, 60804817

Offset: 1

Author

Robert G. Wilson v, Mar 23 2003

Keywords

• nonn

Comments

The first 184 resp. 300 terms of A081430 allow us to deduce 44 resp. 84 consecutive terms of this sequence. - M. F. Hasler, Apr 05 2007

Examples

			a(1) = 14920303 = 1+2*A081430(3)*3 is the smallest 12- prime
		

References

• R. K. Guy, Unsolved Problems in Number Theory, A18.

Links

• M. F. Hasler, Table of n, a(n) for n=1..282

Crossrefs

Cf. A005113, A005105, A005106, A005107, A005108, A081633, A081633, A081635, A081636, A081637, A081638.

Cf. A056637, A081430, A081641.

Programs

Mathematica

PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] - 1]]; ClassMinusNbr[n_] := Length[ NestWhileList[f, n, UnsameQ, All]] - 3; Prime[ Select[ Range[3610000], ClassMinusNbr[ Prime[ # ]] == 12 &]]

PARI

nextclassminus( a, p=1, n=[] )={ while( p, n=concat(n,p); p=0; for( i=1,#a, if( p & 2*a[i] >= p-1, break); for( k=ceil(n[ #n]/2/a[i]),a[ #a]/a[i], if( p & 2*k*a[i] >= p-1, break); if( isprime(2*k*a[i]+1), p=2*k*a[i]+1; break(1+(k==1)); ))));vecextract(n,"^1")}; A081640 = nextclassminus(A081430) \\ M. F. Hasler, Apr 05 2007

Formula

{ a(n) } = { p = 2*m*A081430(k)+1 | k=1,2,...,oo and m=1,2,... such that p is prime and m has no factor of class > 11- } - M. F. Hasler, Apr 05 2007

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 21 2007