A082372 - OEIS

A082372

Primes prime(n) such that there are no solutions to the equation prime(n)^x + prime(n+1)^x = prime(n+2) (mod prime(n+3)) with x an integer.

3, 17, 23, 31, 53, 67, 71, 79, 83, 97, 107, 109, 113, 127, 131, 137, 149, 151, 157, 167, 173, 179, 197, 199, 227, 239, 251, 263, 293, 311, 317, 337, 347, 349, 401, 409, 419, 421, 431, 439, 457, 467, 503, 521, 557, 563, 593, 601, 619, 641, 643, 647

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Is this sequence infinite?

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

17^x + 19^x = 23 (mod 29) has no solutions, therefore 17 is in the sequence.

MATHEMATICA

a = {}; For[n = 1, n < 120, n++, c = 1; For[x = 0, x < Prime[n + 3], x++, If[Mod[Prime[n]^x + Prime[n + 1]^x, Prime[n + 3]] == Prime[n + 2], c = 0]]; If[c == 1, AppendTo[a, Prime[n]]]]; a

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

Sequence in context: A057173 A109371 A272176 * A273407 A267067 A322490

Adjacent sequences: A082369 A082370 A082371 * A082373 A082374 A082375

KEYWORD

nonn

AUTHOR

Cino Hilliard, May 11 2003

EXTENSIONS

Edited by Stefan Steinerberger, Jul 28 2007

STATUS

approved