A123133 - OEIS

%I #8 Dec 03 2013 09:27:10

%S 5,5,12,14,19,24,26,31,36,38,43,49,52,53,58,65,68,69,74,79,84,86,91,

%T 97,100,101,106,111,115,120,122,127,131,137,138,142,149,152,153,158,

%U 163,169,172,173,178,183,187,191,197,198,202,209,210,214,221,222,226,231

%N Sum of pairs of consecutive primes ( p(2n-1)+p(2n) ) and sum of pairs of consecutive nonprime numbers ( np(2n-1)+np(2n) ) in order.

%H A. Frank & P. Jacqueroux, <a href="http://www.paulcooijmans.com/others/intcontest.pdf">International Contest</a>, 2001. Item 13

%e a(1) = 1 + 4 = 5, a(2) = 2 + 3 = 5, a(3) = 5 + 7 = 12, a(4) = 6 + 8 = 14, a(5)= 9 + 10 = 19, a(6) = 11 + 13 = 24, a(7) = 12 + 14 = 26, a(8) = 15 + 16 = 31,...

%t upto=250;Select[Sort[Join[Total/@Partition[Prime[Range[Ceiling[PrimePi[ upto/2]]]], 2],Total/@Partition[Select[Range[Ceiling[upto/2]], !PrimeQ[#]&], 2]]],#<=upto&] (* _Harvey P. Dale_, Aug 25 2011 *)

%o (PARI) nonprimenum=[]; for(n=1,200,if(!isprime(n),nonprimenum=concat(nonprimenum,n))); primenum=[]; forprime(n=1,200,primenum=concat(primenum,n)); nonprimepair=[]; forstep(n=1,length(nonprimenum),2,nonprimepair=concat(nonprimepair,nonprimenum[n]+nonprimenum[n+1])); primepair=[]; forstep(n=1,length(primenum),2,primepair=concat(primepair,primenum[n]+primenum[n+1])); vecsort(concat(nonprimepair,primepair))

%K nonn

%O 1,1

%A Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006