A129888 Start with 10; write down the sum of its digits; add last two terms; repeat.

10, 1, 11, 2, 13, 4, 17, 8, 25, 7, 32, 5, 37, 10, 47, 11, 58, 13, 71, 8, 79, 16, 95, 14, 109, 10, 119, 11, 130, 4, 134, 8, 142, 7, 149, 14, 163, 10, 173, 11, 184, 13, 197, 17, 214, 7, 221, 5, 226, 10, 236, 11, 247, 13, 260, 8, 268, 16, 284, 14, 298, 19, 317, 11, 328, 13

Offset: 1

Author

N. J. A. Sloane, May 26 2007

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007618, A065075.

Programs

Mathematica

nxt[n_]:=Module[{t=Total[n]},{t,Total[IntegerDigits[t]]}]; Flatten[ NestList[ nxt,{10,1},35]] (* Harvey P. Dale, Mar 29 2011 *)

Python

def next2(n): sd = sum(map(int, str(n))); return [sd, n+sd]
def aupton(terms):
    alst = [10]
    while len(alst) < terms: alst.extend(next2(alst[-1]))
    return alst[:terms]
print(aupton(66)) # Michael S. Branicky, Oct 01 2021

Formula

a(2n+1)=A007618(n+2). For 1<=n<=10: a(2n)=A065075(n+1). - R. J. Mathar, Jun 14 2007

Extensions

More terms from R. J. Mathar, Jun 14 2007