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A249630
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Sums of the composite numbers placed between two consecutive prime numbers (A054265), sorted in increasing order.
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1
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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
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OFFSET
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1,2
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COMMENTS
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The first number that occurs more than once is 2592 = a(143) = a(144). - Robert Israel, Nov 11 2014
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LINKS
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MAPLE
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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)]:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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