A081640 - OEIS

%I #12 Sep 24 2018 16:53:14

%S 14920303,18224639,24867247,26532953,34548443,38003011,39800743,

%T 41319599,41443483,45604771,46432667,47247763,49734341,49734493,

%U 49749439,51591833,53014667,55257977,59681383,59700749,60804817

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

%C 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

%D R. K. Guy, Unsolved Problems in Number Theory, A18.

%H M. F. Hasler, <a href="/A081640/b081640.txt">Table of n, a(n) for n=1..282</a>

%F { 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

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

%t 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 &]]

%o (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

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

%Y Cf. A056637, A081430, A081641.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Mar 23 2003

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 21 2007