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A371922 Indices of records in A371921: numbers k such that A371921(k) > A371921(m) for all m < k.

%I A371922 #7 Apr 12 2024 11:40:54
%S A371922 1,12,24,90,204,330,540,1080,1140,2184,3480,6324,15630,23496,38340,
%T A371922 48510,56760,99636,234960,270180,300150,528180,703080,973644,1907178,
%U A371922 5992380,7980930,12032640,20687436,23847642,27465840,28653720,34964340
%N A371922 Indices of records in A371921: numbers k such that A371921(k) > A371921(m) for all m < k.
%C A371922 The corresponding record values are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, ... (see the link for more values).
%H A371922 Amiram Eldar, <a href="/A371922/a371922.txt">Table of n, a(n), A371921(a(n)) for n = 1..33</a>.
%e A371922 The iterations of A033880 over the first 8 terms:
%e A371922  n | a(n) | Iterations
%e A371922  --+------+----------------------------------------------------------------
%e A371922  1 |    1 | 1 -> -1
%e A371922  2 |   12 | 12 -> 4 -> -1
%e A371922  3 |   24 | 24 -> 12 -> 4 -> -1
%e A371922  4 |   90 | 90 -> 54 -> 12 -> 4 -> -1
%e A371922  5 |  204 | 204 -> 96 -> 60 -> 48 -> 28 -> 0
%e A371922  6 |  330 | 330 -> 204 -> 96 -> 60 -> 48 -> 28 -> 0
%e A371922  7 |  540 | 540 -> 600 -> 660 -> 696 -> 408 -> 264 -> 192 -> 124 -> -24
%e A371922  8 | 1080 | 1080 -> 1440 -> 2034 -> 378 -> 204 -> 96 -> 60 -> 48 -> 28 -> 0
%t A371922 ab[n_] := Module[{k}, If[n < 1, 0, k = DivisorSigma[1, n] - 2*n; If[k < 1, 0, k]]]; f[n_] := Module[{s = NestWhileList[ab, n, UnsameQ, All]}, If[s[[-1]] == 0, Length[s] - 2, 0]]; seq[max_] := Module[{fm = 0, f1, s = {}}, Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, max}]; s]; seq[10^5]
%o A371922 (PARI) ab(n) = {my(k); if(n < 1, 0, k = sigma(n) - 2*n; if(k < 1, 0, k));}
%o A371922 f(n) = {my(t = 0); until(bittest(t, n = ab(n)), t += 1<<n); if(n == 0, hammingweight(t) - 1, 0);} \\ after _M. F. Hasler_ at A098007
%o A371922 lista(kmax) = {my(fm = 0, f1); for(k = 1, kmax, f1 = f(k); if(f1 > fm, fm = f1; print1(k, ", "))); }
%Y A371922 Cf. A033880, A098007, A371921.
%K A371922 nonn,more
%O A371922 1,2
%A A371922 _Amiram Eldar_, Apr 12 2024