A123133 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.

5, 5, 12, 14, 19, 24, 26, 31, 36, 38, 43, 49, 52, 53, 58, 65, 68, 69, 74, 79, 84, 86, 91, 97, 100, 101, 106, 111, 115, 120, 122, 127, 131, 137, 138, 142, 149, 152, 153, 158, 163, 169, 172, 173, 178, 183, 187, 191, 197, 198, 202, 209, 210, 214, 221, 222, 226, 231

Offset

1,1

Links

Table of n, a(n) for n=1..58.

A. Frank & P. Jacqueroux, International Contest, 2001. Item 13

Example

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,...

Mathematica

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 *)

Prog

(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))

Crossrefs

Sequence in context: A222681 A061391 A168336 * A328367 A338085 A302676

Adjacent sequences: A123130 A123131 A123132 * A123134 A123135 A123136

Keyword

nonn

Author

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

Status

approved