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Search: id:A082475
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| A082475 |
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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). |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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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.
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PROGRAM
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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))};
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CROSSREFS
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Cf. A082371.
Sequence in context: A022370 A161802 A050850 this_sequence A081767 A093026 A118954
Adjacent sequences: A082472 A082473 A082474 this_sequence A082476 A082477 A082478
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 11 2003
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EXTENSIONS
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Corrected sequence and program Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 09 2009
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