A275160 Least integer k such that A275663(k) = n.

1, 4, 3, 9, 27, 133, 315, 841, 747, 4485, 2799, 14175, 287061, 530079, 3061987, 18371925, 73487701, 195967203

Offset

1,2

Comments

Least integer k such that the number of perfect squares in {k, f(k), f(f(k)),...,1} is equal to n, where f is the Collatz function.

a(n) <= 4^(n-1). - Robert G. Wilson v, Nov 16 2016

a(n) <= (4^(n-1)-1)/3 for n > 2. - Michael S. Branicky, Apr 08 2024

Links

Table of n, a(n) for n=1..18.

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

a(5) = 27 because A275663(27) = 5. The Collatz trajectory of 27 contains the squares 484, 121, 16, 4 and 1. The other values m with the property A275663(m) = 5 are 31, 33, 36, 41, 43, 47, 54, 55, 57, 62, ...

Mathematica

f[n_]:=n/2/; Mod[n, 2]==0; f[n_]:=3 n+1/; Mod[n, 2]==1; g[n_]:=Module[{i, p}, i=n; p=1; While[i>1, If[IntegerQ[Sqrt[i]], p=p+1]; i=f[i]]; p]; Do[k=1; While[g[k]!=m, k++]; Print[m, " ", k], {m, 1, 13}]

Crossrefs

Cf. A006577, A275663.

Sequence in context: A319311 A107381 A242531 * A363469 A369710 A147756

Adjacent sequences: A275157 A275158 A275159 * A275161 A275162 A275163

Keyword

nonn,more

Author

Michel Lagneau, Nov 13 2016

Extensions

a(14)-a(15) from Robert G. Wilson v, Nov 16 2016

a(16)-a(18) from Michael S. Branicky, Apr 08 2024

Status

approved