A082373 Table with 4 consecutive primes prime(k), prime(k+1), prime(k+2) and prime(k+3) in a row such that prime(k)^x + prime(k+1)^x == prime(k+2) (mod prime(k+3)) has no solution x.

3, 5, 7, 11, 17, 19, 23, 29, 23, 29, 31, 37, 31, 37, 41, 43, 53, 59, 61, 67, 67, 71, 73, 79, 71, 73, 79, 83, 79, 83, 89, 97, 83, 89, 97, 101, 97, 101, 103, 107, 107, 109, 113, 127, 109, 113, 127, 131, 113, 127, 131, 137, 127, 131, 137, 139, 131, 137, 139, 149, 137

Offset

1,1

Comments

Note overlapping primes between successive quadruples.

This is a rewriting of A082371 with prime(A082371(n)) building the first column in the table.

Links

Table of n, a(n) for n=1..61.

Example

For prime 17, 17^x + 19^x == 23 (mod 29) has no solutions, which constitutes the 2nd row.
   3,  5,  7, 11;
  17, 19, 23, 29;
  23, 29, 31, 37;
  31, 37, 41, 43;
  53, 59, 61, 67;
  67, 71, 73, 79;
...

Prog

(PARI) \\ No solutions to prime(i)^x+prime(i+1)^x ~= prime(i+2) mod prime(i+3)
noanpbn(m, n) = { for(p=1, m, f=0; for(x=0, n, if((prime(p)^x+prime(p+1)^x-prime(p+2))%prime(p+3)==0, f=1) ); if( f==0, print1(p" ")) ) }

Crossrefs

Cf. A082371.

Sequence in context: A094615 A245396 A144574 * A116959 A249505 A091305

Adjacent sequences: A082370 A082371 A082372 * A082374 A082375 A082376

Keyword

easy,nonn,tabf

Author

Cino Hilliard, May 11 2003

Status

approved