A249630 Sums of the composite numbers placed between two consecutive prime numbers (A054265), sorted in increasing order.

0, 4, 6, 12, 18, 27, 30, 42, 45, 60, 63, 72, 102, 108, 117, 130, 135, 138, 150, 170, 180, 192, 198, 207, 228, 240, 243, 250, 270, 280, 282, 297, 312, 315, 320, 333, 348, 380, 387, 420, 430, 432, 462, 495, 522, 570, 585, 600, 618, 642, 651, 660, 670, 675, 693

Offset: 1

Author

Yves Debeuret, Nov 02 2014

Keywords

• nonn

Comments

The first number that occurs more than once is 2592 = a(143) = a(144). - Robert Israel, Nov 11 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054265.

Programs

Maple

N:= 1000: # to get all terms <= N
Primes:= select(isprime,[2,seq(2*i+1,i=1..floor(N/2))]):
B:= [seq((Primes[i+1]+Primes[i])*(Primes[i+1]-Primes[i]-1)/2, i=1..nops(Primes)-1)]:
sort(select(`<=`,B,N)); # Robert Israel, Nov 11 2014

Mathematica

With[{nn=60},Take[Sort[Total[Range[#[[1]]+1,#[[2]]-1]]&/@Partition[ Prime[ Range[3*nn]],2,1]],nn]] (* Harvey P. Dale, Sep 25 2015 *)

PARI

lista() = {vitp = readvec("c:/gp/bfiles/b029707.txt"); for (k=1, #vitp, v = []; for (n=1, k, vn = vitp[n]; for (j=1, vn, newv = (prime(j+1)+prime(j))*(prime(j+1)-prime(j)-1)/2; if (! vecsearch(v, newv), v = vecsort(concat(v, newv)));););/* to see intermediate results for (i=1, #v, if (v[i] <= newv, print1(v[i], ", "));); print();*/); v;} \\ Michel Marcus, Nov 11 2014

Extensions

More terms from Michel Marcus, Nov 11 2014