A028837 Iterated sum of digits of n is a square.

1, 4, 9, 10, 13, 18, 19, 22, 27, 28, 31, 36, 37, 40, 45, 46, 49, 54, 55, 58, 63, 64, 67, 72, 73, 76, 81, 82, 85, 90, 91, 94, 99, 100, 103, 108, 109, 112, 117, 118, 121, 126, 127, 130, 135, 136, 139, 144, 145, 148, 153, 154, 157, 162, 163, 166, 171, 172, 175, 180

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			E.g. 58 -> 5+8 = 13 -> 1+3 = 4 is a square.
		

Links

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

Crossrefs

Cf. A010888, A028839, A028845.

Programs

Mathematica

LinearRecurrence[{1,0,1,-1},{1,4,9,10},60] (* Harvey P. Dale, Jan 26 2015 *)

Formula

a(n) = a(n-3)+9. If n is a multiple of 3 then a(n) = 3n, otherwise a(n) = 3n-2. Numbers of form {0, 1, 4} modulo 9 - Henry Bottomley, Jun 30 2000

a(1)=1, a(2)=4, a(3)=9, a(4)=10, a(n)=a(n-1)+a(n-3)-a(n-4). - Harvey P. Dale, Jan 26 2015

G.f.: x*(1+3*x+5*x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Sep 22 2016

E.g.f.: (exp(x)*(9*x - 4) + 4*exp(-x/2)*cos(sqrt(3)*x/2))/3. - Stefano Spezia, Mar 07 2024

Extensions

More terms from Patrick De Geest, Jun 15 1999