A092108 Numbers m such that m-th prime + m-th semiprime is prime.

4, 8, 12, 21, 38, 45, 47, 52, 58, 62, 70, 111, 142, 143, 155, 178, 269, 301, 348, 359, 364, 387, 395, 403, 435, 442, 451, 464, 497, 525, 529, 577, 579, 582, 585, 598, 624, 700, 709, 716, 752, 764, 797, 800, 803, 814, 836, 841, 864, 873, 877, 922, 934, 978, 990

Offset: 1

Author

Zak Seidov, Feb 22 2004

Keywords

• nonn

Comments

Resulting primes are: 17, 41, 71, 131, 281, 331, 353, 397, 449, 487, 563, 953, 1279, 1289, 1409, 1627. - Zak Seidov, May 08 2018

Examples

			12 is a member because 12th prime is 37, 12th semiprime is 34 and 37 + 34 = 71 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358.

Programs

Mathematica

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; sp = Select[Range[ 3700], PrimeFactorExponentsAdded[ # ] == 2 &]; p = Table[Prime[i], {i, Length[sp]}]; Select[ Range[ Length[sp]], PrimeQ[ sp[[ # ]] + p[[ # ]]] &] (* Robert G. Wilson v, Feb 24 2004 *)
Module[{nn=5000,sms,prs,len},sms=Select[Range[nn],PrimeOmega[#]==2&];len = Length[sms];prs=Prime[Range[len]];Select[Table[{n,prs[[n]],sms[[n]]},{n,len}], PrimeQ[#[[2]]+#[[3]]]&][[All,1]]] (* Harvey P. Dale, Feb 28 2018 *)

Extensions

More terms from Robert G. Wilson v and Ray Chandler, Feb 24 2004