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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A000040, A001358.

Sequence in context: A190891 A188293 A128233 * A015781 A130643 A014617

Adjacent sequences: A092105 A092106 A092107 * A092109 A092110 A092111

Keyword

nonn

Author

Zak Seidov, Feb 22 2004

Extensions

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

Status

approved