cp's OEIS Frontend

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.

%I A135170 #6 Sep 18 2015 03:46:30
%S A135170 19,29,31,41,43,53,67,71,79,89,101,109,131,149,151,173,197,199,233,
%T A135170 239,241,251,269,271,283,307,311,317,331,337,349,367,401,419,439,449,
%U A135170 461,487,491,499,509,521,593,599,617,641,647,683,691,727,739,751,769,809
%N 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.
%F A135170 {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
%p A135170 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:
%p A135170 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:
%p A135170 A046665 := proc(n) local a,ifs ; a := 0 ; ifs := seq(op(1, i),i=ifactors(n)[2]) ; max(ifs)-min(ifs) ; end:
%p A135170 A111426 := proc(n) A046665(A002808(n)) ; end:
%p A135170 isA135170 := proc(p) local i ; i := isA060254(p) ; if i > 0 then A111426(i) + A111426(i+1) ; isprime(%) ; else false ; fi ; end:
%p A135170 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
%Y A135170 Cf. A111426.
%K A135170 nonn
%O A135170 1,1
%A A135170 _Giovanni Teofilatto_, Feb 14 2008
%E A135170 Corrected and extended by _R. J. Mathar_, Feb 19 2008
%E A135170 More precise definition by _R. J. Mathar_, Sep 17 2009