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Search: id:A135170
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| A135170 |
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Primes equal to the sum of two consecutive composite numbers whose sum of difference between largest and smallest prime factors is prime. |
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2
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| 19, 29, 31, 41, 43, 53, 67, 71, 79, 89, 101, 109, 131, 149, 151, 173, 197, 199, 233, 239, 241, 251, 269, 271, 283, 307, 311, 317, 331, 337, 349, 367, 401, 419, 439, 449, 461, 487, 491, 499, 509, 521, 593, 599, 617, 641, 647, 683, 691, 727, 739, 751, 769, 809
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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{ A060254(j): A002808(i)+A002808(i+1)=A060254(j) and A111426(i)+A111426(i+1) in A000040}. Subsequence of A060254. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2008
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MAPLE
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A002808 := proc(n) option remember ; local a ; if n = 1 then 4; else for a from A002808(n-1)+1 do if not isprime(a) then RETURN(a) ; fi ; od: fi ; end: isA060254 := proc(n) local i, sComp ; if isprime(n) then for i from 1 do sComp := A002808(i)+A002808(i+1) ; if sComp = n then RETURN(i); elif sComp > n then RETURN(-1) ; fi ; od: else -1 ; fi ; end: A046665 := proc(n) local a, ifs ; a := 0 ; ifs := seq(op(1, i), i=ifactors(n)[2]) ; max(ifs)-min(ifs) ; end: A111426 := proc(n) A046665(A002808(n)) ; end: isA135170 := proc(p) local i ; i := isA060254(p) ; if i > 0 then A111426(i) + A111426(i+1) ; isprime(%) ; else false ; fi ; end: for n from 1 to 300 do p := ithprime(n) ; if isA135170(p) then printf("%d, ", p) ; fi ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2008
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CROSSREFS
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Cf. A111426.
Adjacent sequences: A135167 A135168 A135169 this_sequence A135171 A135172 A135173
Sequence in context: A052260 A067833 A140566 this_sequence A139539 A047985 A061763
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KEYWORD
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nonn,uned
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Feb 14 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 19 2008
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