A139693 -id:A139693 - cp's OEIS frontend

A324920 a(n) is the number of iterations of the integer splitting function (A056737) necessary to reach zero.

0, 1, 2, 3, 1, 2, 2, 3, 3, 1, 4, 5, 2, 3, 3, 3, 1, 2, 4, 5, 2, 2, 2, 3, 3, 1, 6, 3, 4, 5, 2, 3, 2, 4, 4, 3, 1, 2, 3, 5, 4, 5, 2, 3, 4, 2, 3, 4, 3, 1, 3, 4, 2, 3, 4, 3, 2, 2, 4, 5, 2, 3, 6, 3, 1, 4, 3, 4, 4, 3, 4, 5, 2, 3, 4, 5, 4, 2, 4, 5, 3, 1, 6, 7, 3, 3, 6, 7, 4, 5, 2, 3, 6, 5, 3, 4, 2, 3, 4, 3, 1, 2, 6, 7, 3

Offset: 0

Robert G. Wilson v, Mar 20 2019

nonn

The iterations always fall to zero, proof by induction: 0 is 0; 1 -> 0; 2 -> 1; 3 -> 2; 4 -> 2; n -> some number less than n.

First occurrence of k >= 0: 0, 1, 2, 3, 10, 11, 26, 83, 178, ... see A324921.

			a(0) = 0;
a(1) = 1 since 1 -> 0;
a(2) = 2 since 2 -> 1 -> 0;
a(3) = 3 since 3 -> 2 -> 1 -> 0;
a(4) = 1 since 4 -> 0; etc.

Cf. A056737, A139693, A324921.

g[n_] := Block[{d = Divisors@n}, len = Length@d; If[ OddQ@ len, 0, d[[1 + len/2]] - d[[len/2]]]]; f[n_] := Length@ NestWhileList[f, n, # > 0 &] -1; Array[f, 105, 0]

a056737(n)=n=divisors(n); n[(2+#n)\2]-n[(1+#n)\2] \\ after M. F. Hasler in A056737
a(n) = my(x=n, i=0); while(x!=0, i++; x=a056737(x)); i \\ Felix Fröhlich, Mar 20 2019

a(n) = 1 iff n is a perfect square (A000290).

A139694 a(0)=1. a(n) = smallest positive integer m, m > a(n-1), where, for k divides m, minimum(|k -m/k|) = n. a(n) = the minimum positive integer m where A056737(m) = n and m > a(n-1).

Original entry on oeis.org

1, 2, 3, 10, 21, 50, 55, 78, 105, 136, 171, 242, 253, 338, 351, 406, 465, 578, 595, 666, 741, 820, 903, 1058, 1081, 1250, 1275, 1378, 1653, 1682, 1711, 1830, 1953, 2178, 2211, 2556, 2701, 2738, 2775, 2926, 3081, 3362, 3403, 3698, 3741, 3916, 4232, 4418, 4465

Offset: 0

Leroy Quet, Apr 29 2008

nonn

Cf. A056737, A139693.

a056737(n)={n=divisors(n); n[(2+#n)\2]-n[(1+#n)\2];} \\ from A056737
lista(nn) = {olda = 1; for (n=1, nn+1, print1(olda, ", "); newa = olda + 1; while (a056737(newa) != n, newa++); olda = newa;);} \\ Michel Marcus, Feb 11 2014

More terms from Michel Marcus, Feb 11 2014

cp's OEIS Frontend

A324920 a(n) is the number of iterations of the integer splitting function (A056737) necessary to reach zero.

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