cp's OEIS Frontend

A161165 The n-th twin prime plus the n-th isolated prime.

%I A161165 #12 Feb 01 2019 19:58:00
%S A161165 5,28,44,58,66,84,98,112,120,138,156,186,192,228,236,268,276,318,332,
%T A161165 370,390,406,414,456,474,498,510,528,536,580,588,606,614,648,654,670,
%U A161165 680,712,722,786,792,868,878,898,912,948,954,1020,1026,1078,1112,1146,1158,1180
%N A161165 The n-th twin prime plus the n-th isolated prime.
%F A161165 a(n) = A001097(n) + A007510(n).
%e A161165 a(1) = 3 +  2 =  5;
%e A161165 a(2) = 5 + 23 = 28;
%e A161165 a(3) = 7 + 37 = 44.
%p A161165 isA001097 := proc(n) isprime(n) and (isprime(n+2) or isprime(n-2)) ; end proc:
%p A161165 A001097 := proc(n) if n = 1 then 3; else for p from procname(n-1)+2 by 2 do if isA001097(p) then return p end if; end do: end if; end proc:
%p A161165 isA007510 := proc(n) isprime(n) and not isprime(n+2) and not isprime(n-2) ; end proc:
%p A161165 A007510 := proc(n) if n = 1 then 2; else for p from procname(n-1)+1 do if isA007510(p) then return p end if; end do: end if; end proc:
%p A161165 A161165 := proc(n) A001097(n) + A007510(n) ; end proc:
%p A161165 seq(A161165(n),n=1..100) ; # _R. J. Mathar_, Mar 18 2010
%p A161165 # alternate program
%p A161165 isA001097 := proc(n) if isprime(n) then isprime(n+2) or isprime(n-2) ; else false; end if; end proc:
%p A161165 isA007510 := proc(n) if isprime(n) then not isprime(n+2) and not isprime(n-2) ; else false; end if; end proc:
%p A161165 A001097 := proc(n) option remember; if n = 1 then 3; else for a from procname(n-1)+1 do if isA001097(a) then return a; end if; end do: end if; end proc:
%p A161165 A007510 := proc(n) option remember; if n = 1 then 2; else for a from procname(n-1)+1 do if isA007510(a) then return a; end if; end do: end if; end proc:
%p A161165 A161165 := proc(n) A001097(n)+A007510(n) ; end proc: seq(A161165(n),n=1..90) ; # _R. J. Mathar_, Mar 29 2010
%Y A161165 Cf. A001097, A007510.
%K A161165 nonn,easy
%O A161165 1,1
%A A161165 _Juri-Stepan Gerasimov_, Jun 04 2009
%E A161165 Entries checked by _R. J. Mathar_, Mar 18 2010