A007612 a(n+1) = a(n) + digital root (A010888) of a(n).

1, 2, 4, 8, 16, 23, 28, 29, 31, 35, 43, 50, 55, 56, 58, 62, 70, 77, 82, 83, 85, 89, 97, 104, 109, 110, 112, 116, 124, 131, 136, 137, 139, 143, 151, 158, 163, 164, 166, 170, 178, 185, 190, 191, 193, 197, 205, 212, 217, 218, 220, 224, 232, 239, 244, 245, 247, 251

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Keywords

• nonn
• base
• easy
• nice

Comments

Take m, a natural number. If m == 1 (mod 6), then for every n a(m)*a(n) is in A007612. - Ivan N. Ianakiev, May 08 2013

References

• J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 65.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Digital Root.

Crossrefs

Cf. A004207, A010888, A029898, A064806.

Programs

Haskell

a007612 n = a007612_list !! (n-1)
a007612_list = iterate a064806 1  -- Reinhard Zumkeller, Apr 13 2013

Maple

A007612 := proc(n) option remember: if(n=1)then return 1: fi: return procname(n-1) + ((procname(n-1)-1) mod 9) + 1: end: seq(A007612(n), n=1..100); # Nathaniel Johnston, May 04 2011

Mathematica

dr[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]; NestList[#+dr[#]&, 1,60] (* Harvey P. Dale, Sep 24 2011 *)
NestList[#+Mod[#,9]&,1,60] (* Harvey P. Dale, Sep 14 2016 *)

PARI

first(n)=my(v=vector(n)); v[1]=1; for(k=2,n, v[k]=v[k-1]+v[k-1]%9); v \\ Charles R Greathouse IV, Jun 25 2017

PARI

a(n)=n\6*27 + [-4,1,2,4,8,16][n%6+1] \\ Charles R Greathouse IV, Jun 25 2017

Formula

a(1) = 1, a(n+1) = a(n) + a(n) mod 9. - Reinhard Zumkeller, Mar 23 2003

First differences are [1,2,4,8,7,5] repeated. - M. F. Hasler, Sep 15 2009; corrected by John Keith, Aug 17 2022

n == 1, 2, 4, 8, 16, or 23 (mod 27). - Dean Hickerson, Mar 25 2003

Limit_{n->oo} a(n)/n = 9/2; A029898(n) = a(n+1) - a(n) = A010888(a(n)). - Reinhard Zumkeller, Feb 27 2006

a(6n+1)=27n+1, a(6n+2)=27n+2, a(6n+3)=27n+4, a(6n+4)=27n+8, a(6n+5)=27n+16, a(6n+6)=27n+23. - Franklin T. Adams-Watters, Mar 13 2006

G.f.: (1+4*x^4+3*x^3+x^2)/((x+1)*(x^2-x+1)*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

a(n+1) = A064806(a(n)). - Reinhard Zumkeller, Apr 13 2013