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Search: id:A075560
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| A075560 |
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a(1) = 1, a(n) = smallest number greater than the previous term which can not be obtained as the sum of products of any group of earlier terms. |
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+0
1
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| 1, 2, 4, 10, 22, 50, 106, 230, 480, 1054, 2656, 6782, 17254
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Next term is > 37000. - David Wasserman (wasserma(AT)spawar.navy.mil), Jan 20 2005
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EXAMPLE
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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.
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PROGRAM
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(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)); (Wasserman)
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CROSSREFS
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Sequence in context: A091618 A018108 A033497 this_sequence A078040 A164990 A121285
Adjacent sequences: A075557 A075558 A075559 this_sequence A075561 A075562 A075563
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KEYWORD
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hard,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 24 2002
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EXTENSIONS
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Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Jan 20 2005
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