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A007612
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a(n+1) = a(n) + digital root (A010888) of a(n).
(Formerly M1114)
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12
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Digital Root.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A004207, A010888, A029898, A064806.
Sequence in context: A262224 A058961 A130917 * A112395 A004207 A219675
Adjacent sequences: A007609 A007610 A007611 * A007613 A007614 A007615
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein
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STATUS
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approved
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