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Search: id:A105403
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| A105403 |
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Numbers n such that prime(n)-1 and prime(n+1)-1 have the same largest prime factor. |
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1
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OFFSET
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1,1
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COMMENT
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The PARI program below is a generalization of this type of sequence. These numbers are rare. Are they finite? Proof?
No more terms between 217 and 3090000. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
No more terms < 5760000. - David Wasserman (dwasserm(AT)earthlink.net), May 02 2008
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FORMULA
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{i: A023503(i) = A023503(i+1)}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2008
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EXAMPLE
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The prime factors of prime(217)-1 = 2, 3, 13, 17. The prime factors of prime(218)-1 = 2, 2, 2, 2, 5, 17 and 17 is the same largest factor.
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PROGRAM
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(PARI) \prime indices such that gd of prime(x)+ k and prime(x+m) + k are equal divpm1(n, m, k) = { local(x, l1, l2, v1, v2); for(x=2, n, v1 = ifactor(prime(x)+ k); v2 = ifactor(prime(x+m)+k); l1 = length(v1); l2 = length(v2); if(v1[l1] == v2[l2], print1(x", ") ) ) } ifactor(n) = \Vector of the prime factors of n { local(f, j, k, flist); flist=[]; f=Vec(factor(n)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }
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CROSSREFS
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Sequence in context: A113695 A098827 A078208 this_sequence A134644 A085637 A157870
Adjacent sequences: A105400 A105401 A105402 this_sequence A105404 A105405 A105406
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KEYWORD
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hard,more,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 01 2005
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