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A294174
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Numbers that can be expressed both as the sum of first primes and as the sum of first composites.
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2
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0, 10, 1988, 14697, 83292, 1503397, 18859052, 93952013, 89171409882, 9646383703961, 209456854921713, 3950430820867201, 13113506646374409451778
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OFFSET
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1,2
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LINKS
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EXAMPLE
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10 is in the sequence because prime(1) + prime(2) + prime(3) = 2 + 3 + 5 = 10 and composite(1) + composite(2) = 4 + 6 = 10 (where composite(i) is the i-th composite number).
1988 is in the sequence because Sum_{i=1..33} prime(i) = A007504(33) = Sum_{i=1..51} composite(i) = A053767(51) = 1988.
== ======== ======== =================
1 0 0 0
2 3 2 10
3 33 51 1988
4 80 147 14697
5 175 361 83292
6 660 1582 1503397
7 2143 5699 18859052
8 4556 12821 93952013
9 118785 403341 89171409882
10 1131142 4229425 9646383703961
11 5012372 19786181 209456854921713
12 20840220 86192660 3950430820867201 (End)
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MATHEMATICA
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nextComposite[n_] := Block[{k = n + 1}, While[PrimeQ@k, k++]; k]; c = sc = 4; p = sp = 2; lst = {0}; While[p < 1000000000, If[ sc == sp, AppendTo[lst, sc]; c = nextComposite@c; sc += c]; While[ sp < sc, p = NextPrime@ p; sp += p]; While[ sc < sp, c = nextComposite@ c; sc += c]]; lst (* Robert G. Wilson v, Feb 11 2018 *)
Module[{pr=Accumulate[Prime[Range[5*10^7]]], co=Accumulate[Select[ Range[ 11*10^7], CompositeQ]]}, Join[ {0}, Intersection[pr, co]]] (* The program generates the first 12 terms of the sequence; to generate the 13th term increase the Range specifications substantially, but the program will take a long time to run. *) (* Harvey P. Dale, Sep 17 2019 *)
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CROSSREFS
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KEYWORD
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nonn,more,nice
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AUTHOR
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STATUS
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approved
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