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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A037660 A122600 A063682 * A065059 A198584 A342815

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

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Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)