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

1, 12, 24, 90, 204, 330, 540, 1080, 1140, 2184, 3480, 6324, 15630, 23496, 38340, 48510, 56760, 99636, 234960, 270180, 300150, 528180, 703080, 973644, 1907178, 5992380, 7980930, 12032640, 20687436, 23847642, 27465840, 28653720, 34964340

Offset

1,2

Comments

The corresponding record values are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, ... (see the link for more values).

Links

Table of n, a(n) for n=1..33.

Amiram Eldar, Table of n, a(n), A371921(a(n)) for n = 1..33.

Example

The iterations of A033880 over the first 8 terms:
 n | a(n) | Iterations
 --+------+----------------------------------------------------------------
 1 |    1 | 1 -> -1
 2 |   12 | 12 -> 4 -> -1
 3 |   24 | 24 -> 12 -> 4 -> -1
 4 |   90 | 90 -> 54 -> 12 -> 4 -> -1
 5 |  204 | 204 -> 96 -> 60 -> 48 -> 28 -> 0
 6 |  330 | 330 -> 204 -> 96 -> 60 -> 48 -> 28 -> 0
 7 |  540 | 540 -> 600 -> 660 -> 696 -> 408 -> 264 -> 192 -> 124 -> -24
 8 | 1080 | 1080 -> 1440 -> 2034 -> 378 -> 204 -> 96 -> 60 -> 48 -> 28 -> 0

Mathematica

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]

Prog

(PARI) ab(n) = {my(k); if(n < 1, 0, k = sigma(n) - 2*n; if(k < 1, 0, k)); }
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
lista(kmax) = {my(fm = 0, f1); for(k = 1, kmax, f1 = f(k); if(f1 > fm, fm = f1; print1(k, ", "))); }

Crossrefs

Cf. A033880, A098007, A371921.

Sequence in context: A109745 A364726 A226493 * A051385 A290304 A289335

Adjacent sequences: A371919 A371920 A371921 * A371923 A371924 A371925

Keyword

nonn,more

Author

Amiram Eldar, Apr 12 2024

Status

approved