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Search: id:A105308
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| A105308 |
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Indices n of primes p(n), p(n+2) such that p(n)-1 and p(n+2)-1 have the same largest prime factor. |
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+0
2
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OFFSET
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2,1
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COMMENT
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These numbers are rare. Are they finite? Proof?
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EXAMPLE
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The prime factors of prime(45)-1 = 2, 2, 7, 7
the prime factors of prime(47)-1 = 2, 3, 5, 7
and 7 is the common largest factor.
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MATHEMATICA
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t = {0, 0, 0}; Do[ t = {t[[2]], t[[3]], FactorInteger[ Prime[n + 2] - 1][[ -1, 1]]}; If[ t[[1]] == t[[3]], Print[n]], {n, 195000000}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2005)
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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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Cf. A105404.
Adjacent sequences: A105305 A105306 A105307 this_sequence A105309 A105310 A105311
Sequence in context: A047811 A091280 A066155 this_sequence A116983 A078426 A114413
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KEYWORD
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more,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 01 2005
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EXTENSIONS
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a(8) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2005
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