A356675 Lexicographically earliest infinite sequence satisfying a(1) > -1 and a(n-1) = A075826(a(n)).
1, 5, 9, 16, 27, 38, 48, 58, 66, 76, 87, 98, 117, 136, 155, 177, 198, 215, 235, 254, 275, 295, 310, 333, 350, 372, 394, 411, 433, 452, 474, 495, 514, 535, 555, 576, 598, 615, 635, 650, 669, 689, 705, 728, 749, 773, 795, 810, 833, 850, 872, 894, 913, 934, 950, 973, 994, 1013, 1034, 1050, 1071, 1093
Offset: 1
Examples
A075826 yields the number of letters in US English spelling of each number subtracted from the number's value. For example, A075826(5) yields 1, because 5 - 4 (F-I-V-E) is 1. Our formula reveals that if 5 is in our sequence, it must come immediately after 1, which it does. However, 4, which must come immediately after 0, is not in our sequence, which we can prove because there exists no number k such that A075826(k) = 4. Each number less than the largest known value in this sequence produces a finite sequence unless it is in this sequence, because some number eventually is a dead end like 4.
Links
- Michel Marcus, Table of n, a(n) for n = 1..11623
Programs
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PARI
f(k) = k - A005589(k); listd(nn) = {nn *= 2; my(vs = vector(nn)); my(list = List()); my(m=1, lbound = 0); listput(list, m); while (m < nn, if (vs[m] == 0, vs[m] = Vec(select(x->(x==m), vector(100, k, f(k+m-1)), 1)); if (#vs[m], vs[m] = apply(x->(x+m-1), vs[m]))); my(ok = 1, vc = vs[m]); if (! #vc, ok = 0, vc = select(x->(x>lbound), vc); if (! #vc, ok = 0);); if (!ok, lbound = list[#list]; listpop(list); if (! #list, return()); m = list[#list];, lbound = 0; m = vc[1]; listput(list, m););); Vec(select(x->(x<=nn/2), list));} \\ Michel Marcus, Aug 31 2022
Formula
a(n-1) = A075826(a(n)).
Comments