A082374 Set of n such that the prime quadruple prime(n), prime(n+1), prime(n+2), prime(n+3) does not have a solution for the congruence prime(n+1)^x - prime(n)^x == prime(n+2) mod prime(n+3).

2, 6, 16, 17, 18, 20, 21, 25, 29, 31, 33, 35, 36, 41, 45, 52, 53, 59, 61, 62, 64, 65, 77, 79, 81, 83, 84, 85, 88, 90, 91, 94, 95, 96, 100, 101, 102, 103, 104, 106, 110, 114, 116, 117, 119, 122, 132, 136, 137, 139, 147, 152, 154, 155, 156, 157, 158, 164, 167, 172, 173

Offset

1,1

Links

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

Example

2 is in the sequence because prime(2)=3, prime(2+1)=5, prime(2+2)=7, prime(2+3)=11 and 5^x-3^x == 7 mod 11 has no solutions.

Prog

(PARI) \\ Solutions to prime(i+1)^x-prime(i+1)^x == prime(i+2) mod prime(i+3).
noanmbn(m, n) = { for(p=1, m, f=0; for(x=0, n, if((prime(p+1)^x-prime(p)^x-prime(p+2))%prime(p+3)==0, f=1) ); if(f==0, print1(p ", ")) ) }

Crossrefs

Cf. A082371.

Sequence in context: A355096 A036046 A080622 * A085226 A260376 A330866

Adjacent sequences: A082371 A082372 A082373 * A082375 A082376 A082377

Keyword

easy,nonn

Author

Cino Hilliard, May 11 2003

Status

approved