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A331800 a(1) = 1; 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 = 0 or 1. 1
1, 3, 5, 7, 17, 19, 50, 64, 152, 190, 470, 598, 1448, 1828, 4472, 5668, 13796, 17452, 42584, 53920, 131408, 166312, 405560, 513400, 1251584, 1584208, 3862592, 4889392, 11920400, 15088816, 36788000, 46566784, 113532416, 143710048, 350376032, 443509600, 1081305728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inserting the additional term a(0) = 2 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..37.

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

Eric Weisstein's World of Mathematics, Complete Sequence

PROG

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

upto(lim)={my(a=[1], 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. A331809, A331811.

Sequence in context: A001259 A248370 A087126 * A062547 A125739 A219461

Adjacent sequences:  A331797 A331798 A331799 * A331801 A331802 A331803

KEYWORD

nonn

AUTHOR

Zhandos Mambetaliyev, Jan 26 2020

EXTENSIONS

a(13)-a(14) from Hugo Pfoertner, Jan 27 2020

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

STATUS

approved

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Last modified September 20 07:46 EDT 2020. Contains 337264 sequences. (Running on oeis4.)