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A075560 a(1) = 1, a(n) is the smallest number greater than the previous term that cannot be obtained as the sum of products of any group of earlier terms. 0
1, 2, 4, 10, 22, 50, 106, 230, 480, 1054, 2656, 6782, 17254 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Next term is > 37000. - David Wasserman, Jan 20 2005
LINKS
EXAMPLE
a(5) = 22, as using 1, 2, 4 and 10 the following numbers can be generated: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 40, 41, 42, 43, 80 and 81. E.g., 19 = 10 + 2*4 + 1.
PROG
(PARI) canMake(n, v) = local(l, newV, m, c, count, mm, x); if (n < 0, return(0)); if (n == 0, return(1)); l = length(v); if (l == 0, return(0)); newV = vector(l - 1, i, v[i]); if (canMake(n, newV), return(1)); m = v[l]; c = l - 1; if (canMake(n - m, newV), return(1)); while (c && v[c]*m > n, c--); for (i = 1, 2^c - 1, count = 0; mm = m; x = i; for (j = 1, c, if (x%2, mm *= v[j], count++; newV[count] = v[j]); x \= 2); for (j = c + 1, l - 1, newV[j - c + count] = v[j]); if (canMake (n - mm, vector(l - 1 - c + count, q, newV[q])), return(1))); 0; v = [2]; n = 4; while (1, if (canMake(n, v), n += 2, l = length(v); newV = vector(l + 1); for (i = 1, l, newV[i] = v[i]); newV[l + 1] = n; v = newV; print(n); n = 2*n + 2)); \\ David Wasserman, Jan 20 2005
CROSSREFS
Sequence in context: A260916 A192627 A275445 * A078040 A240041 A164990
KEYWORD
nonn,hard,more
AUTHOR
Amarnath Murthy, Sep 24 2002
EXTENSIONS
Corrected and extended by David Wasserman, Jan 20 2005
Offset corrected by Mohammed Yaseen, Jul 21 2023
STATUS
approved

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Last modified February 21 09:51 EST 2024. Contains 370228 sequences. (Running on oeis4.)