A331809 - OEIS

A331809

a(1) = 1; a(2) = 2; thereafter a(n) is the smallest number > a(n-1) which is neither of the form 2*a(i) nor Sum_{j=1..n-1} ( b_j*a(j) ) where 0 < i < n, b_j = 1 or 0.

1, 2, 5, 9, 13, 31, 35, 92, 118, 280, 350, 866, 1102, 2668, 3368, 8240, 10444, 25420, 32156, 78464, 99352, 242128, 306440, 747272, 945976, 2306128, 2919008, 7117088, 9009040, 21964144, 27802160, 67784384, 85802464, 209191168, 264795488, 645591584, 817196512, 1992379072

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Inserting the additional term a(0) = 3 would result in a so-called complete sequence after sorting. (The sorted sequence will then meet Brown's criterion.)

LINKS

Table of n, a(n) for n=1..38.

Eric Weisstein's World of Mathematics, Brown's Criterion

Eric Weisstein's World of Mathematics, Complete Sequence

PROG

(PARI) /* a(n) for 0<n */

upto(lim)={my(a=[1, 2], b=[]); for(i=1, lim, forsubset(#a, x, b=concat(b, [vecsum(vecextract(a, x))])); b=setminus(vecsort(b, , 8), a); for(j=1, #a, b=concat(b, [2*a[j]]); b=vecsort(b, , 8)); if(setsearch(b, i)==0, a=concat(a, [i]); a=vecsort(a, , 8)) ); a}

{ upto(200) }

CROSSREFS

Cf. A126326, A331800, A331811.

Sequence in context: A325647 A367403 A049753 * A126326 A364248 A284916

Adjacent sequences: A331806 A331807 A331808 * A331810 A331811 A331812

KEYWORD

nonn

AUTHOR

Zhandos Mambetaliyev, Jan 27 2020

EXTENSIONS

a(12)-a(15) from Hugo Pfoertner, Jan 27 2020

More terms, using Rémy Sigrist's C++ at A331811 from Hugo Pfoertner, Jan 28 2020

STATUS

approved