A092952 Smallest unhappy number that takes n iterations of the sum of the squares of digits to reach 4, which is the smallest number of the unhappy numbers cycle.

4, 2, 11, 113, 78, 58, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3, 36, 6, 29, 16, 4, 2, 9, 3

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Unhappy Numbers

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Formula

From Colin Barker, Jul 11 2019: (Start)

G.f.: x*(4 + 2*x + 11*x^2 + 113*x^3 + 78*x^4 + 58*x^5 + 29*x^6 + 16*x^7 - 2*x^10 - 110*x^11 - 42*x^12 - 52*x^13) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).

a(n) = a(n-8) for n>8.

(End)

Example

113 is the fourth number of the sequence because it takes 4 iterations to reach 4: 113 / 1^2 + 1^2 + 3^2 = 11 / 1^2 + 1^2 = 2 / 2^2 = 4.

Prog

(PARI) Vec(x*(4 + 2*x + 11*x^2 + 113*x^3 + 78*x^4 + 58*x^5 + 29*x^6 + 16*x^7 - 2*x^10 - 110*x^11 - 42*x^12 - 52*x^13) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^80)) \\ Colin Barker, Jul 11 2019

Crossrefs

Sequence in context: A094406 A142706 A361216 * A286145 A010318 A188134

Adjacent sequences: A092949 A092950 A092951 * A092953 A092954 A092955

Keyword

nonn,base,easy

Author

Sergio Pimentel, Apr 23 2004

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010

Status

approved