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A082373
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Table with 4 consecutive primes prime(k), prime(k+1), prime(k+2) and prime(k+3) in a row such that prime(k)^x + prime(k+1)^x == prime(k+2) (mod prime(k+3)) has no solution x.
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0
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3, 5, 7, 11, 17, 19, 23, 29, 23, 29, 31, 37, 31, 37, 41, 43, 53, 59, 61, 67, 67, 71, 73, 79, 71, 73, 79, 83, 79, 83, 89, 97, 83, 89, 97, 101, 97, 101, 103, 107, 107, 109, 113, 127, 109, 113, 127, 131, 113, 127, 131, 137, 127, 131, 137, 139, 131, 137, 139, 149, 137
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Note over lapping primes between successive quadruples.
This is a rewriting of A082371 with prime(A082371(n)) building the first column in the table.
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EXAMPLE
| For prime 17, 17^x + 19^x == 23 (mod 29) has no solutions, which constitutes the 2nd row.
3,5,7,11;
17,19,23,29;
23,29,31,37;
31,37,41,43;
53,59,61,17;
67,71,73,79;
...
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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" ")) ) }
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CROSSREFS
| Cf. A082371.
Sequence in context: A019449 A094615 A144574 * A116959 A091305 A164319
Adjacent sequences: A082370 A082371 A082372 * A082374 A082375 A082376
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), May 11 2003
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