A131188 Indices of products of twin primes in the semiprimes.

6, 13, 48, 103, 270, 508, 1001, 1413, 2724, 3052, 4859, 5668, 8029, 9062, 9608, 12558, 13828, 17319, 18823, 22781, 28077, 40162, 42359, 48113, 60703, 71793, 79161, 83792, 90129, 94954, 140436, 144445, 146452, 156704, 165199, 218110, 223095

Offset: 1

Author

Zak Seidov, Sep 25 2007

Keywords

• nonn

Examples

			Ignoring (2, 3), the first twin prime pair is (3, 5). We have 3 * 5 = 15, which is the sixth semiprime (the previous five semiprimes being 4, 6, 9, 10, 14). Hence 6 is the first term of this sequence.
The second twin prime pair is (5, 7). Then 5 * 7 = 35, which is the thirteenth semiprime (following 21, 22, 25, 26, 33, 34). Hence 13 is the second term of this sequence.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A128301.

Programs

Maple

N:= 10^7: # to use semiprimes <= N
P:= select(isprime, [2,seq(i,i=3..N/2,2)]):
count:= 0:
for i from 1 to numtheory:-pi(floor(sqrt(N))) do
  for j from i to nops(P) while P[i]*P[j] <= N do
    count:= count+1;
    S[count]:= [P[i]*P[j],evalb(P[j]-P[i]=2)]
od od:
S:= sort(convert(S,list),(a,b) -> a[1] S[t][2],[$1..nops(S)]); # Robert Israel, Dec 30 2015

Mathematica

s = Select[Range[10^6], PrimeOmega@ # == 2 &]; Map[Position[s, #] &, # (# + 2) &@ Select[Prime@ Range@ 160, NextPrime@ # - # == 2 &]] // Flatten (* Michael De Vlieger, Dec 31 2015 *)
Module[{upto=2*10^6,sp,tp},sp=Select[Range[upto],PrimeOmega[#]==2&]; tp= Times@@@Select[Partition[Prime[Range[upto/2]],2,1],#[[2]]-#[[1]] == 2&]; Table[Position[sp,n],{n,tp}]]//Flatten (* Harvey P. Dale, Nov 03 2016 *)

Formula

{i: A001358(i) = A001359(k) * A006512(k), for some k > 0}. - R. J. Mathar, Oct 26 2007

Extensions

More terms from R. J. Mathar, Oct 26 2007