1,2

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).

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.

(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);

(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

Cf. A002049.

Sequence in context: A057129 A036404 A018498 this_sequence A067941 A092265 A163295

Adjacent sequences: A002045 A002046 A002047 this_sequence A002049 A002050 A002051

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2006