Search: id:A075560
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%I A075560
%S A075560 1,2,4,10,22,50,106,230,480,1054,2656,6782,17254
%N A075560 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.
%C A075560 Next term is > 37000. - David Wasserman (wasserma(AT)spawar.navy.mil), 
               Jan 20 2005
%e A075560 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.
%o A075560 (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)
%Y A075560 Sequence in context: A091618 A018108 A033497 this_sequence A078040 A164990 
               A121285
%Y A075560 Adjacent sequences: A075557 A075558 A075559 this_sequence A075561 A075562 
               A075563
%K A075560 hard,nonn
%O A075560 0,2
%A A075560 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 24 2002
%E A075560 Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), 
               Jan 20 2005

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