|
%I #37 May 11 2018 02:01:16
%S 4,8,12,21,38,45,47,52,58,62,70,111,142,143,155,178,269,301,348,359,
%T 364,387,395,403,435,442,451,464,497,525,529,577,579,582,585,598,624,
%U 700,709,716,752,764,797,800,803,814,836,841,864,873,877,922,934,978,990
%N Numbers m such that m-th prime + m-th semiprime is prime.
%C Resulting primes are: 17, 41, 71, 131, 281, 331, 353, 397, 449, 487, 563, 953, 1279, 1289, 1409, 1627. - _Zak Seidov_, May 08 2018
%H Charles R Greathouse IV, <a href="/A092108/b092108.txt">Table of n, a(n) for n = 1..10000</a>
%e 12 is a member because 12th prime is 37, 12th semiprime is 34 and 37 + 34 = 71 is prime.
%t 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 *)
%t 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 *)
%Y Cf. A000040, A001358.
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 22 2004
%E More terms from _Robert G. Wilson v_ and _Ray Chandler_, Feb 24 2004
|
