A135170 Primes equal to a sum c1+c2 of two consecutive composite numbers such that lpf(c1)-spf(c1)+lpf(c2)-spf(c2) from their largest and smallest prime factors is prime.

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

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Formula

{A060254(j): A002808(i)+A002808(i+1)=A060254(j) and A111426(i)+A111426(i+1) in A000040}. Subsequence of A060254. - R. J. Mathar, Feb 19 2008

Maple

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, Feb 19 2008

Crossrefs

Cf. A111426.

Sequence in context: A254330 A052260 A067833 * A173959 A370139 A139539

Adjacent sequences: A135167 A135168 A135169 * A135171 A135172 A135173

Keyword

nonn

Author

Giovanni Teofilatto, Feb 14 2008

Extensions

Corrected and extended by R. J. Mathar, Feb 19 2008

More precise definition by R. J. Mathar, Sep 17 2009

Status

approved