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 A057663 Primes p such that p + 2^p is also a prime. 4
 3, 5, 89, 317, 701 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Different from A056206, where, e.g., at n=89, 89 is not minimal, A056206(89)=29 and not 89. a(6) > 27479. - Ralf Stephan, Oct 23 2002 Intersection of A000040 and A052007. - Iain Fox, Nov 08 2017 a(6) > 678561. - Iain Fox, Nov 08 2017 Every term other than 3 is congruent to 5 (mod 6). - Arkadiusz Wesolowski, Nov 14 2017 These terms satisfy phi(k + 2^k) = phi(k) + 2^k, where phi is A000010, the Euler totient function. Conjecture: this sequence gives all numbers k that satisfy the condition phi(k + 2^k) = phi(k) + 2^k. - Juri-Stepan Gerasimov, May 23 2019 LINKS EXAMPLE q=3, 2^3 + 3 = 11 a prime. MATHEMATICA Select[Prime@ Range[10^3], PrimeQ[# + 2^#] &] (* Michael De Vlieger, Nov 08 2017 *) PROG (PARI) lista(nn) = forprime(p=3, nn, if(ispseudoprime(p + 2^p), print1(p, ", "))) \\ Iain Fox, Nov 13 2017 (MAGMA) [p: p in PrimesUpTo(1000) | IsPrime(2^p+p) ] // Vincenzo Librandi, Aug 07 2010 (Sage) [n for n in (1..1000) if is_prime(n) and is_prime(2^n+n)] # G. C. Greubel, May 24 2019 CROSSREFS Cf. A000010, A006127, A056206, A056208, A057664, A057665. Sequence in context: A133660 A271925 A236365 * A056244 A173487 A279310 Adjacent sequences:  A057660 A057661 A057662 * A057664 A057665 A057666 KEYWORD nonn,hard,more AUTHOR Labos Elemer, Oct 16 2000 STATUS approved

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Last modified July 31 23:46 EDT 2021. Contains 346377 sequences. (Running on oeis4.)