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

1,1

Links

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

Formula

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

Example

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.

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]<b[1]):
select(t -> 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 *)

Crossrefs

Cf. A128301.

Sequence in context: A353964 A041489 A239530 * A247939 A203977 A003757

Adjacent sequences: A131185 A131186 A131187 * A131189 A131190 A131191

Keyword

nonn

Author

Zak Seidov, Sep 25 2007

Extensions

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

Status

approved