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A002048
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Segmented numbers, or prime numbers of measurement.
(Formerly M0972 N0363)
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6
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1, 2, 4, 5, 8, 10, 14, 15, 16, 21, 22, 25, 26, 28, 33, 34, 35, 36, 38, 40, 42, 46, 48, 49, 50, 53, 57, 60, 62, 64, 65, 70, 77, 80, 81, 83, 85, 86, 90, 91, 92, 100, 104, 107, 108, 116, 119, 124, 127, 132, 133, 137, 141, 144, 145, 148, 150, 151, 154, 158, 159, 163, 165
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| G. E. Andrews, MacMahon's prime numbers of measurement, Amer. Math. Monthly, 82 (1975), 922-923.
R. K. Guy, Unsolved Problems in Number Theory, E30.
P. A. MacMahon, The prime numbers of measurement on a scale, Proc. Camb. Phil. Soc. 21 (1923), 651-654; reprinted in Coll. Papers I, pp. 797-800.
Problem E1910, Amer. Math. Monthly, 75 (1968), 80-81.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..7836
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MAPLE
| (Maple program from R. J. Mathar, Jun 04 2006) A002048 := proc(anmax::integer, printlist::boolean)
local a, asum, su, i, piv, j;
a := [];
for i from 1 to anmax do
a := [op(a), i];
od:
if printlist then
printf("%d %d\n", 1, a[1]);
printf("%d %d\n", 2, a[2]);
fi;
asum := [a[1]+a[2], a[2]];
for i from 3 to anmax do
asum := [op(asum), 0];
od:
piv := 3;
while piv <= nops(a) do
for i from 1 to piv-2 do
a := remove(has, a, asum[i]);
od:
if printlist then
printf("%a %a\n", piv, a[piv]);
fi;
for i from 1 to piv do
asum := subsop(i=asum[i]+a[piv], asum);
od:
piv := piv+1;
od;
RETURN(a);
end:
A002048(40000, true);
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MATHEMATICA
| A002048[anmax_] := (a = {}; Do[ AppendTo[a, i], {i, 1, anmax}]; asum = {a[[1]] + a[[2]], a[[2]]}; Do[AppendTo[asum, 0], {i, 3, anmax}]; piv = 3; While[ piv <= Length[a], Do[a = DeleteCases[a, asum[[i]]], {i, 1, piv-2}]; Do[ asum[[i]] += a[[piv]] , {i, 1, piv}]; piv = piv+1; ]; a); A002048[63] (* From Jean-François Alcover, Jul 28 2011, converted from R. J. Mathar's Maple prog. *)
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PROG
| (C++) #include <iostream> #include <vector> #include <algorithm> #define NMAX 400 using namespace std; int main(int argc, char *argv[]) { vector<int> a; for(int i=0; i< NMAX; i++) a.push_back(i+1); for(int piv=2; piv < a.size(); piv++) for(int i=0; i < piv-1 && i < a.size()-1; i++) { int su= a[i]+a[i+1]; remove(a.begin(), a.end(), su); for(int j=i+2; j < piv && j < a.size(); j++) { su += a[j]; remove(a.begin(), a.end(), su); if(su > NMAX) break; } } for(int i=0; i < a.size() && a[i] < NMAX; i++) cout << a[i] << ", "; return 0; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2006
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CROSSREFS
| Cf. A002049.
Sequence in context: A036404 A186077 A018498 * A174989 A190809 A067941
Adjacent sequences: A002045 A002046 A002047 * A002049 A002050 A002051
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2006
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