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Search: id:A108137
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| A108137 |
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Primes p such that p + 6^k is composite for all k >= 0. |
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+0
1
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| 3, 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 919, 929
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The PARI code given suggests that these values are merely conjectures. - njas, Jun 30 2005
Except for the first term, these primes are of the form 10n+9. It follows that 10n+9 + (5+1)^k = 5H not prime for some H for all n and k.
Superset of A030433. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 24 2008]
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PROGRAM
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(PARI) pplus2ton(n, m, b) = \defiant primes base b { local(k, s, p, y, flag); s=0; forprime(p=2, n, flag=1; for(k=0, m, y=p+b^k; if(ispseudoprime(y), \ print1(k, ", "); s++; flag=0; break) ); if(flag, print1(p", ")); \search for defiant primes. ); print(); print(s); }
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CROSSREFS
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Adjacent sequences: A108134 A108135 A108136 this_sequence A108138 A108139 A108140
Sequence in context: A070045 A063557 A062619 this_sequence A102978 A107165 A066811
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Jun 27 2005
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