A336772 -id:A336772 - cp's OEIS frontend

A336773 a(n) is the least prime of the form 2^j*3^k + 1, j > 0, k > 0, j + k = n. a(n) = 0 if no such prime exists.

7, 13, 37, 73, 97, 193, 577, 769, 3457, 10369, 0, 12289, 629857, 839809, 147457, 995329, 1990657, 786433, 5308417, 120932353, 14155777, 28311553, 0, 113246209, 29386561537, 3439853569, 6879707137, 1811939329, 18345885697, 3221225473, 1253826625537, 0, 85691213438977

Offset: 2

Hugo Pfoertner, Aug 28 2020

nonn

Robert Israel, Table of n, a(n) for n = 2..2193

Cf. A033845, A058383, A336772 (positions of 0).

f:= proc(n) local k,p;
   for k from 1 to n-1 do
     p:= 2^(n-k)*3^k+1;
     if isprime(p) then return p fi
   od;
   0
end proc:
map(f, [$2..40]); # Robert Israel, Aug 30 2020

for(n=2,34, my(pm=oo); for(j=1,n-1, my(k=n-j,p=2^j*3^k+1);if(isprime(p),pm=min(p,pm))); print1(if(pm==oo,0,pm),", "))

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

A337424 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

12, 19, 20, 23, 26, 33, 34, 35, 40, 41, 48, 51, 52, 54, 63, 68, 69, 74, 75, 78, 83, 87, 93, 97, 101, 103, 105, 114, 116, 123, 132, 135, 138, 141, 142, 144, 147, 152, 154, 159, 165, 170, 172, 173, 179, 180, 186, 187, 189, 192, 194, 202, 203, 210, 215, 216, 217, 218, 221

Offset: 1

Hugo Pfoertner, Aug 27 2020

nonn

Positions of 0 in A337423.

Cf. A336772, A337426.

cp's OEIS Frontend

A336773 a(n) is the least prime of the form 2^j*3^k + 1, 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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Author

Keywords

Links

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Programs

Maple

A337424 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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Author

Keywords

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