%I A002048 M0972 N0363
%S A002048 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,
%T A002048 53,57,60,62,64,65,70,77,80,81,83,85,86,90,91,92,100,104,107,108,116,
%U A002048 119,124,127,132,133,137,141,144,145,148,150,151,154,158,159,163,165
%N A002048 Segmented numbers, or prime numbers of measurement.
%D A002048 G. E. Andrews, MacMahon's prime numbers of measurement, Amer. Math. Monthly, 
               82 (1975), 922-923.
%D A002048 R. K. Guy, Unsolved Problems in Number Theory, E30.
%D A002048 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.
%D A002048 Problem E1910, Amer. Math. Monthly, 75 (1968), 80-81.
%D A002048 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002048 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002048 R. J. Mathar, <a href="b002048.txt">Table of n, a(n) for n = 1..7836</
               a>
%H A002048 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeNumberofMeasurement.html">Link to a section of The World of 
               Mathematics.</a>
%p A002048 (Maple program from R. J. Mathar, Jun 04 2006) A002048 := proc(anmax::integer,
               printlist::boolean)
%p A002048 local a, asum,su,i,piv,j;
%p A002048 a := [];
%p A002048 for i from 1 to anmax do
%p A002048 a := [op(a),i];
%p A002048 od:
%p A002048 if printlist then
%p A002048 printf("%d %d\n",1,a[1]);
%p A002048 printf("%d %d\n",2,a[2]);
%p A002048 fi;
%p A002048 asum := [a[1]+a[2],a[2]];
%p A002048 for i from 3 to anmax do
%p A002048 asum := [op(asum),0];
%p A002048 od:
%p A002048 piv := 3;
%p A002048 while piv <= nops(a) do
%p A002048 for i from 1 to piv-2 do
%p A002048 a := remove(has,a, asum[i]);
%p A002048 od:
%p A002048 if printlist then
%p A002048 printf("%a %a\n",piv,a[piv]);
%p A002048 fi;
%p A002048 for i from 1 to piv do
%p A002048 asum := subsop(i=asum[i]+a[piv], asum);
%p A002048 od:
%p A002048 piv := piv+1;
%p A002048 od;
%p A002048 RETURN(a);
%p A002048 end:
%p A002048 A002048(40000,true);
%o A002048 (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
%Y A002048 Cf. A002049.
%Y A002048 Sequence in context: A057129 A036404 A018498 this_sequence A067941 A092265 
               A163295
%Y A002048 Adjacent sequences: A002045 A002046 A002047 this_sequence A002049 A002050 
               A002051
%K A002048 nonn,nice
%O A002048 1,2
%A A002048 N. J. A. Sloane (njas(AT)research.att.com).
%E A002048 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2006