A362132 -id:A362132 - cp's OEIS frontend

A362133 Smallest indices k where A362131(k) = A362132(n).

1, 3, 5, 7, 9, 12, 17, 31, 36, 41, 58, 74, 82, 112, 160, 189, 198, 220, 294, 325, 914, 1267, 1389, 1872, 1927, 1957, 2032, 2155, 2184, 2302, 2358, 2835, 3047, 3672, 3794, 3832, 3873, 3924, 4543, 4785, 35502, 98365, 1728198, 8375015

Offset: 1

Michael De Vlieger, Apr 10 2023

Next term exceeds 2^28, if it exists.

Michael De Vlieger, Plot (log_2 a(n), A362132(n)) at (x, y).

Cf. A360179, A362131, A362132.

nn = 2^20;
c[] := False; q[] := False; h[] := 0; f[n] := DivisorSigma[0, n];
a[1] = j = u = w = 1;
{1}~Join~Rest@ Reap[Do[
      If[c[j],
        k = j + f[u]; h[j]++; h[u]--,
        k = f[j]; c[j] = True; h[j]++ ];
      u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
      While[h[u] == 0, u++];
      If[k == w, While[q[w], w++]; Sow[n]], {n, 2, nn}] ][[-1, -1]]

A362131 a(n) = smallest missing number u in A360179(1..n).

Original entry on oeis.org

2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21

Offset: 1

Michael De Vlieger, Apr 10 2023

nonn

Michael De Vlieger, Table of n, a(n) for n = 1..40000
Michael De Vlieger, Labeled scatterplot of A360179(n), n = 1..300, showing a(n) in small red dots, and A360179(n) in large red when A360179(n) = a(n-1).

Cf. A000005, A360179, A362132.

nn = 120; c[] := False; q[] := False; h[] := 0; f[n] := DivisorSigma[0, n];
a[1] = j = u = w = 1;
{2}~Join~Reap[Do[
     If[c[j],
       k = j + f[u]; h[j]++; h[u]--,
       k = f[j]; c[j] = True; h[j]++ ];
     u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
     While[h[u] == 0, u++]; If[k == w, While[q[w], w++]];
     Sow[w], {n, 2, nn}] ][[-1, -1]]

cp's OEIS Frontend

A362133 Smallest indices k where A362131(k) = A362132(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica