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 A243734 Primes p for which p + 4, p^2 + 4 and p^3 + 4 are primes. 1
 3, 7, 103, 277, 487, 967, 4783, 5503, 5923, 8233, 21013, 26317, 27943, 41593, 55213, 78307, 78853, 86197, 89653, 94723, 99013, 123727, 148153, 157177, 166627, 172867, 177883, 179107, 185893, 192883, 194713, 203767, 204517, 223633, 225217, 227593, 236893 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a subset of the sequences: A023200: Primes p such that p + 4 is also prime. A243583: Primes p for which p + 4 and p^3 + 4 are primes. p is either 2 mod 5 or 3 mod 5, hence p^4 + 4 is 0 mod 5. LINKS Abhiram R Devesh, Table of n, a(n) for n = 1..1000 EXAMPLE p = 3 is in this sequence because p + 4 = 7, p^2 + 4 = 13 and p^3 + 4 = 31 are all primes. p  : p+4,  p^2+4,     p^3+4 7  :  11,     53,       347 103: 107,  10613,   1092731 277: 281,  76733,  21253937 487: 491, 237173, 115501307 PROG (Python) import sympy.ntheory as snt n=2 while n>1: ....n1=n+4 ....n2=((n**2)+4) ....n3=((n**3)+4) ....##Check if n1, n2 and n3 are also primes. ....if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n2)== True: ........print(n, " , " , n1, " , ", n2, " , ", n3) ....n=snt.nextprime(n) (PARI) s=[]; forprime(p=2, 200000, if(isprime(p+4) && isprime(p^2+4) && isprime(p^3+4), s=concat(s, p))); s \\ Colin Barker, Jun 11 2014 CROSSREFS Cf. A023200, A243583. Sequence in context: A159310 A299377 A129660 * A158467 A260824 A028414 Adjacent sequences:  A243731 A243732 A243733 * A243735 A243736 A243737 KEYWORD nonn,easy AUTHOR Abhiram R Devesh, Jun 09 2014 STATUS approved

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Last modified February 26 05:19 EST 2020. Contains 332276 sequences. (Running on oeis4.)