A082376 First of quadruple of consecutive primes p1,p2,p3,p4 such that the congruence p2^x - p1^x == p3 (mod p4) has no solution.

3, 13, 53, 59, 61, 71, 73, 97, 109, 127, 137, 149, 151, 179, 197, 239, 241, 277, 283, 293, 311, 313, 389, 401, 419, 431, 433, 439, 457, 463, 467, 491, 499, 503, 541, 547, 557, 563, 569, 577, 601, 619, 641, 643, 653, 673, 743, 769, 773, 797, 853, 881, 887, 907, 911, 919, 929, 971, 991, 1021, 1031

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For the prime quadruple 3,5,7,11, 5^x-3^x == 7 (mod 11) has no solutions.

Maple

Res:= NULL: count:= 0:
p1:= 2: p2:= 3: p3:= 5: p4:= 7:
while count < 100 do
  found:= false;
  for x from 1 to p4-2 do
    if p2 &^ x - p1 &^ x - p3 mod p4 = 0 then found:= true; break fi
  od:
  if not found then Res:= Res, p1; count:= count+1 fi;
  p1:= p2: p2:= p3: p3:= p4: p4:= nextprime(p4);
od:
Res; # Robert Israel, Mar 18 2018

Crossrefs

Cf. A082371.

Sequence in context: A122600 A063682 A346409 * A065059 A198584 A346382

Adjacent sequences: A082373 A082374 A082375 * A082377 A082378 A082379

Keyword

easy,nonn

Author

Cino Hilliard, May 11 2003

Extensions

Name clarified by Robert Israel, Mar 18 2018

Status

approved