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 A321084 Primes prime(n) such that 1 + Sum_{k=1..n} 2^(prime(k)-1) is prime. 0
 2, 3, 5, 19, 2039, 2879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes prime(n) such that A080355(n+1) is prime. The prime p = 19 gives the prime 332887 = 1010001010001010111_2. The positions of 1's from the end are 1, 2, 3, 5, 7, 11, 13, 17, 19. Let S(n) = Sum_{k=1..n} 2^(prime(k)-1). Conjecture: q(n) = 1 + S(n) is prime if and only if 2^S(n) == 1 (mod q(n)). LINKS EXAMPLE a(3) = 5 since 1 + 2^(2-1) + 2^(3-1) + 2^(5-1) = 10111_2 = 23 is prime. Note that prime(3) = 5 and A080355(3+1) = 23 prime. MATHEMATICA Prime@ Select[Range[10^3], PrimeQ[1 + Total@ Array[2^(Prime[#] - 1) &, #]] &] (* Michael De Vlieger, Oct 31 2018 *) PROG (PARI) isok(p) = isprime(p) && isprime(1 + sum(k=1, primepi(p), 2^(prime(k)-1))); \\ Michel Marcus, Oct 27 2018 CROSSREFS Cf. A000040, A000043, A080355, A113878. Sequence in context: A128363 A106047 A048826 * A054798 A127078 A184252 Adjacent sequences: A321081 A321082 A321083 * A321085 A321086 A321087 KEYWORD nonn,more AUTHOR Thomas Ordowski, Oct 27 2018 EXTENSIONS a(5)-a(6) from Robert Israel, Oct 27 2018 STATUS approved

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Last modified March 26 23:21 EDT 2023. Contains 361553 sequences. (Running on oeis4.)