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 A007612 a(n+1) = a(n) + digital root (A010888) of a(n). (Formerly M1114) 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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. FORMULA a(1) = 1, a(n+1) = a(n) + a(n) mod 9. - Reinhard Zumkeller, Mar 23 2003 First differences are [1,2,4,8,5,7] repeated. - M. F. Hasler, Sep 15 2009 n == 1, 2, 4, 8, 16, or 23 (mod 27). - Dean Hickerson, Mar 25 2003 Lim a(n)/n = 9/2 for n --> oo; 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) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009] a(n+1) = A064806(a(n)). - 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 *) PROG (Haskell) a007612 n = a007612_list !! (n-1) a007612_list = iterate a064806 1  -- Reinhard Zumkeller, Apr 13 2013 (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 CROSSREFS Cf. A004207. Sequence in context: A262224 A058961 A130917 * A112395 A004207 A219675 Adjacent sequences:  A007609 A007610 A007611 * A007613 A007614 A007615 KEYWORD nonn,base,easy,nice AUTHOR STATUS approved

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)