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A002048 Segmented numbers, or prime numbers of measurement.
(Formerly M0972 N0363)
7
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; text; internal format)
OFFSET

1,2

REFERENCES

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.

Š. Porubský, On MacMahon's segmented numbers and related sequences. Nieuw Arch. Wisk. (3) 25 (1977), no. 3, 403--408. MR0485763 (58 #5575)

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).

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..7836

G. E. Andrews, MacMahon's prime numbers of measurement, Amer. Math. Monthly, 82 (1975), 922-923.

R. L. Graham and C. B. A. Peck, Problem E1910, Amer. Math. Monthly, 75 (1968), 80-81.

R. K. Guy, Letter to G. E. Andrews, Apr 14 1975

Eric Weisstein's World of Mathematics, Prime Number of Measurement.

FORMULA

Andrews conjectures that lim_{n -> oo} n log n / (a(n) loglog n) = 1. - N. J. A. Sloane, Dec 01 2013

MAPLE

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);

# R. J. Mathar, Jun 04 2006

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] (* Jean-François Alcover, Jul 28 2011, converted from R. J. Mathar's Maple prog. *)

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, May 31 2006 */

(Haskell)

import Data.List ((\\))

a002048 n = a002048_list !! (n-1)

a002048_list = f [1..] [] where

   f (x:xs) ys = x : f (xs \\ scanl (+) x ys) (x : ys)

-- Reinhard Zumkeller, May 23 2013

CROSSREFS

Cf. A002049 (partial sums), A004978, A005242, A033627.

Sequence in context: A036404 A186077 A018498 * A174989 A190809 A067941

Adjacent sequences:  A002045 A002046 A002047 * A002049 A002050 A002051

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. J. Mathar, May 31 2006

STATUS

approved

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Last modified December 6 03:18 EST 2016. Contains 278772 sequences.