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A092108 Numbers m such that m-th prime + m-th semiprime is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 11:29 EST 2022. Contains 350454 sequences. (Running on oeis4.)