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a(1) = 1; thereafter a(n) is the next smallest number after > a(n-1) which cannot be represented in is neither of the form 2*a(i) and nor Sum_{j=1..n-1} ( b_j*a(j) ) where 0 < i < n, b_j = 1 0 or 0. a(1) = 1. Inserting the additional term a(0) = 2 results in a so-called complete sequence after sorting.

2, 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

0,1

1,2

Inserting the additional term a(0) = 2 would result in a so-called complete sequence after sorting. (The sorted sequence, from smallest to largest, will then meet Brown's criterion.)

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nonn,more,changed

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a(n) is the next number after a(n-1) which cannot be represented in the form 2*a(i) and Sum_{j=1..n-1} ( b_j*a(j) ) where 0 < i < n, b_j = 1 or 0. The a(1) = 1. Inserting the additional term a(0) = 2 results in a so-called complete sequence starts: a(0) = 2; a(1) = 1after sorting.

2, 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

This sequence is a complete sequence.

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

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a(0) = 2; a(1) = 1; a(n) = is the next number after a(n-1) which cannot be represented in the form 2*a(i) and Sum_{j=1..n-1} ( b_j*a(j) ) where 0 < i < n, b_j = 1 or 0. The sequence starts: a(0) = 2; a(1) = 1.

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}

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

(PARI) 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}

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