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A354414
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a(n) is the smallest positive integer which does not occur in any Lucas sequence in which the first term is at most n and the second term is at most the first term.
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1
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1, 4, 9, 17, 25, 38, 51, 64, 85, 106, 127, 148, 169, 203, 237, 271, 305, 339, 373, 407, 441, 496, 551, 606, 661, 716, 771, 826, 881, 936, 991, 1046, 1101, 1156, 1245, 1334, 1423, 1512, 1601, 1690, 1779, 1868, 1957, 2046, 2135, 2224, 2313, 2402, 2491, 2580, 2669, 2758, 2847, 2936
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OFFSET
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0,2
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LINKS
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PROG
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(PARI) a(n) = {if (n==0, return(1)); my(seqs=vector(n*(n+1)/2), k=0, all = List()); for (i=1, n, for (j=1, i, k++; seqs[k] = List([i, j]); listput(all, i); listput(all, j); ); ); while (1, my(s=seqs[#seqs], m = s[#s-1] + s[#s]); for (i=1, #seqs, my(ss = seqs[i], new); while((new = ss[#ss-1] + ss[#ss]) <= m, listput(seqs[i], new); listput(all, new); ss = seqs[i]); ); listsort(all, 1); my(vall = Vec(all), m=0); for (i=1, vecmax(vall), if (!vecsearch(vall, i), m = i; break); ); if (m && (m <= seqs[#seqs][#seqs[#seqs]]), return(m)); ); } \\ Michel Marcus, May 26 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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