A082475 Prime index i for consecutive primes p(i),p(i+1),p(i+2),p(i+3) that do not have a solution for the congruences p(i)^x+p(i+1)^x = p(i+2) mod p(i+3) and p(i+1)^x-p(i)^x = p(i+2) mod p(i+3).
2, 16, 20, 25, 29, 31, 33, 35, 36, 41, 45, 52, 62, 64, 79, 81, 83, 85, 88, 91, 96, 102, 103, 110, 114, 116, 117, 119, 122, 136, 154, 155, 164, 167, 172, 173, 183, 185, 188, 190, 211, 218, 219, 220, 225, 229, 232, 233, 234, 238, 246, 249, 252, 256, 262, 276, 277
Offset: 1
Keywords
Examples
For primes 3,5,7,11: 3^x+5^x = 7 mod 11 has no solutions. 5^x-3^x = 7 mod 11 has no solutions.
Crossrefs
Cf. A082371.
Programs
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PARI
list_A082475(lim)={my(f,p0=2,p1=3,p2=5,p3=7);for(p=1,lim,f=0;for(x=0, p3-1,if((p0^x + p1^x)%p3 == p2 || (p1^x-p0^x)%p3 == p2, f=1;break));if(f==0, print1(p","));p0=p1;p1=p2;p2=p3;p3=prime(p+4))};
Extensions
Corrected sequence and program Charles R Greathouse IV, Oct 09 2009