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

Author

Giovanni Teofilatto, Feb 14 2008

Keywords

• nonn

Crossrefs

Cf. A111426.

Programs

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

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

Extensions

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

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