A337424 -id:A337424 - cp's OEIS frontend

A337423 a(n) is the least prime of the form (3^j*5^k - 1)/2, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.

7, 37, 67, 337, 607, 3037, 15187, 27337, 49207, 683437, 0, 131835937, 659179687, 19929037, 35872267, 228881835937, 2491129687, 0, 0, 311391210937, 12013549804687, 0, 235357947067, 1176789735337, 0, 10591107618037, 52955538090187, 5675104819335937, 608185958862304687

Offset: 2

Hugo Pfoertner, Aug 27 2020

nonn

Cf. A093625, A076481, A337424, A337425, A337426.

A337425 a(n) is the least prime of the form (3^j*5^k + 1)/2, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.

Original entry on oeis.org

0, 23, 113, 563, 1013, 1823, 70313, 351563, 82013, 410063, 43945313, 1328603, 18452813, 1977539063, 0, 830376563, 538084013, 968551223, 13452100313, 1441625976563, 43584805013, 2145767211914063, 0, 0, 9806581127813, 6354664570823, 681012578320313, 441296150751563, 0

Offset: 2

Hugo Pfoertner, Aug 27 2020

nonn

Cf. A093625, A076481, A337423, A337424, A337426.

A337426 Sums s of positive exponents such that no prime of the form (3^j*5^k + 1)/2 with j + k = s exists.

Original entry on oeis.org

2, 16, 24, 25, 30, 40, 41, 50, 57, 61, 64, 65, 69, 71, 74, 77, 79, 80, 82, 84, 89, 95, 97, 99, 104, 105, 106, 107, 111, 112, 119, 124, 129, 132, 133, 136, 137, 139, 141, 143, 147, 153, 155, 158, 165, 166, 167, 168, 170, 176, 177, 178, 181, 193, 203, 208, 215, 216

Offset: 1

Hugo Pfoertner, Aug 27 2020

nonn

Robert Israel, Table of n, a(n) for n = 1..800

Positions of 0 in A337425.

Cf. A336772, A337424.

filter:= proc(n) local k, p;
   for k from 1+(n-1 mod 2) to n-1 by 2 do
     p:= (3^(n-k)*5^k+1)/2;
     if isprime(p) then return false fi
   od;
   true
end proc:
select(filter, [$2..300]); # Robert Israel, Sep 01 2020

cp's OEIS Frontend

A337423 a(n) is the least prime of the form (3^j*5^k - 1)/2, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.

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A337425 a(n) is the least prime of the form (3^j*5^k + 1)/2, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.

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A337426 Sums s of positive exponents such that no prime of the form (3^j*5^k + 1)/2 with j + k = s exists.

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