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%I #14 Sep 08 2022 08:45:17
%S 1,6,12,20,22,24,28,30,34,56,60,142,144,148,168,192,196,230,252,260,
%T 276,282,304,322,334,344,346,352,366,374,380,386,394,404,418,424,432,
%U 440,444,470,478,484,572,590,610,612,630,642,662,684,754,766,784,790,840,842,874,886
%N Numbers n such that n*prime(n)+(n+1)*prime(n+1)+(n+2)*prime(n+2) is prime.
%H Michael S. Branicky, <a href="/A105455/b105455.txt">Table of n, a(n) for n = 1..10000</a>
%e n=1: 1*prime(1) + 2*prime(2) + 3*prime(3) = 1*2 + 2*3 + 3*5 = 23 prime,
%e n=6: 6*prime(6) + 7*prime(7) + 8*prime(8) = 6*13 + 7*17 + 8*19 = 349 prime. - _Zak Seidov_, Feb 18 2016
%t bb={};Do[If[PrimeQ[n Prime[n]+(n+1) Prime[n+1]+(n+2) Prime[n+2]], bb=Append[bb, n]], {n, 1, 400}];bb
%t Select[Range@ 900, PrimeQ[# Prime[#] + (# + 1) Prime[# + 1] + (# + 2) Prime[# + 2]] &] (* _Michael De Vlieger_, Feb 05 2016 *)
%o (PARI) lista(nn) = {for(n=1, nn, if(ispseudoprime(n*prime(n)+(n+1)*prime(n+1)+(n+2)*prime(n+2)), print1(n, ", "))); } \\ _Altug Alkan_, Feb 05 2016
%o (Magma) [n: n in [1..1000] | IsPrime(n*NthPrime(n)+(n+1)*NthPrime(n+1)+(n+2)*NthPrime(n+2))]; // _Vincenzo Librandi_, Feb 06 2016
%o (Python)
%o from itertools import islice
%o from sympy import isprime, nextprime
%o def agen(): # generator of terms
%o m, p, q, r = 1, 2, 3, 5
%o while True:
%o t = m*p + (m+1)*q + (m+2)*r
%o if isprime(t): yield m
%o m, p, q, r = m+1, q, r, nextprime(r)
%o print(list(islice(agen(), 58))) # _Michael S. Branicky_, May 17 2022
%Y Cf. A033286, A105454, A152117, A119487.
%K nonn
%O 1,2
%A _Zak Seidov_, May 02 2005
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