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Search: id:A083370
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| A083370 |
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Primes satisfying f(2p)=p when f(1)=5 (see comment). |
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+0
6
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| 23, 31, 47, 53, 61, 73, 83, 89, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 359, 367, 373, 383, 389, 401, 409, 421, 433, 443, 449, 467, 479, 491
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture : start from any initial value f(1)>=2 and define f(n) to be the largest prime factor of f(1)+f(2)+...+f(n-1); then f(n)=n/2+O(log(n)) and there are infinitely primes p such that f(2p)=p.
Coincides with A124582 in the first 154 terms: a(154)=A124582(154)=1723, but a(155,156,..)=1777, 1783, 1801, 2017, 3251,..., whereas A124582(155,156,...)=1733, 1741, 1747,... - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2007
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MAPLE
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A006530 := proc(n) if n = 1 then RETURN(1) ; else RETURN(op(1, op(-1, op(2, ifactors(n))))) ; fi ; end: f := proc(n) option remember ; if n = 1 then RETURN(5) ; else A006530(add(f(i), i=1..n-1)) ; fi ; end: isA083370 := proc(p) if isprime(p) then if p = f(2*p) then true ; else false ; fi ; else false ; fi ; end: n := 1 : i := 1 : while n <= 1000 do p := ithprime(i) ; if isA083370(p) then printf("%d %d ", n, p) ; n := n+ 1 ; fi ; i := i+1 ; end: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2007
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CROSSREFS
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Cf. A076973.
Sequence in context: A106312 A023679 A107662 this_sequence A124582 A130796 A031924
Adjacent sequences: A083367 A083368 A083369 this_sequence A083371 A083372 A083373
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2003
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