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 A181628 Numbers k such that (2^k + 3^k)/13 is prime. 2
 6, 10, 14, 22, 34, 38, 82, 106, 218, 334, 4414, 7246, 10118, 10942, 15898, 42422 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are of the form 2p, p prime. The prime (2^4414 + 3^4414)/13 = 79300327387 ...611266 985181 has 2105 decimal digits. LINKS Table of n, a(n) for n=1..16. EXAMPLE 10 is in the sequence because (2^10+ 3^10)/13 = 60073/13 = 4621 is prime. MAPLE with(numtheory):for n from 1 to 4500 do: x:= (2^n + 3^n)/13:if floor(x)=x and type(x, prime)=true then printf(`%d, `, n):else fi:od: # alternative Res:= NULL: p:= 2: while p < 6000 do p:= nextprime(p); if isprime((2^(2*p)+3^(2*p))/13) then Res:= Res, 2*p fi; od: Res; # Robert Israel, Apr 26 2017 PROG (PARI) is(n)=n%2==0 && isprime(n/2) && ispseudoprime((2^n+3^n)/13) \\ Charles R Greathouse IV, Jun 06 2017 (Python) from sympy import isprime def afind(limit, startk=1): k = startk pow2 = 2**k pow3 = 3**k for k in range(startk, limit+1): q, r = divmod(pow2+pow3, 13) if r == 0 and isprime(q): print(k, end=", ") pow2 *= 2 pow3 *= 3 afind(1000) # Michael S. Branicky, Dec 28 2021 CROSSREFS Cf. A057469. Sequence in context: A207574 A278972 A241817 * A023387 A315236 A315237 Adjacent sequences: A181625 A181626 A181627 * A181629 A181630 A181631 KEYWORD nonn,more AUTHOR Michel Lagneau, Nov 18 2010 EXTENSIONS a(12) from D. S. McNeil, Nov 18 2010 a(13) and a(14) from Robert Israel, Apr 26 2017 a(15) from Michael S. Branicky, Dec 28 2021 a(16) from Michael S. Branicky, Apr 26 2023 STATUS approved

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Last modified April 14 12:23 EDT 2024. Contains 371661 sequences. (Running on oeis4.)