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Search: id:A105406
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| A105406 |
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Indices n of primes p(n), p(n+3) such that p(n)+1 and p(n+3)+1 have the same largest prime factor. |
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| 29, 53, 92, 126, 204, 281, 333, 489, 573, 816, 1169, 1585, 1885, 13906, 24059, 44421, 48142, 53394, 84043, 474045, 489910, 535841, 2135727, 3095936, 3925702, 4858924, 6618689, 8537111, 58246902, 163424560, 188474341, 193910248, 785107460, 847979055, 6040627719, 7900840637
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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No other term <=210000. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 13 2006
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MAPLE
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with(numtheory): a:=proc(n) local a, b: a:=factorset(1+ithprime(n)): b:=factorset(1+ithprime(n+3)): if a[nops(a)]=b[nops(b)] then n else fi end: seq(a(n), n=1..10000); # it takes hours - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 13 2006
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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: A042947 A134555 A117328 this_sequence A124284 A054822 A034847
Adjacent sequences: A105403 A105404 A105405 this_sequence A105407 A105408 A105409
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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 01 2005
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EXTENSIONS
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One more term from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 13 2006
a(21)-a(37) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 03 2008
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