A354414 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.

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

Offset

0,2

Links

Table of n, a(n) for n=0..53.

Hajime Katsumoto, An Amazing Pattern involving Lucas Sequences, Crux Mathematicorum, Vol. 48(5), May 2022, pp. 279-280.

Prog

(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

Crossrefs

Cf. A000032, A000045, A354415.

Sequence in context: A092464 A377389 A328271 * A173562 A161320 A170879

Adjacent sequences: A354411 A354412 A354413 * A354415 A354416 A354417

Keyword

nonn

Author

Michel Marcus, May 26 2022

Status

approved