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Search: id:A105404
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| A105404 |
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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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| 1, 2, 3, 5, 7, 8, 22, 23, 259, 3598, 4808, 7715, 8821, 9155, 10765, 29745, 1776197, 2417850, 11568019, 1617124497, 5632000774
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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The prime factors of prime(22)+1 = 2, 2, 2, 2, 5
the prime factors of prime(24)+1 = 2, 3, 3, 5
and 5 is the common largest prime factor.
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MATHEMATICA
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t = {0, 3, 2}; Do[ t = {t[[2]], t[[3]], FactorInteger[Prime[n + 2] + 1][[ -1, 1]]}; If[t[[1]] == t[[3]], Print[n]], {n, 20000000}] (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. A105308.
Adjacent sequences: A105401 A105402 A105403 this_sequence A105405 A105406 A105407
Sequence in context: A080435 A108330 A039892 this_sequence A075012 A067090 A139790
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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(1), a(17), a(18) & a(19) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2005
a(20), a(21) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 03 2008
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