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A030139
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a(n+1) = sum of digits of (a(n) + a(n-1)).
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0
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1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3, 2, 5, 7, 3, 1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3, 2, 5, 7, 3, 1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3, 2, 5, 7, 3, 1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3, 2, 5, 7, 3, 1, 4, 5
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OFFSET
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0,2
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COMMENTS
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This is also the digital root of A022378, Fibonacci starting with 2 and 32, beginning from the 20th term 2: [2, 5, 7, 3, 1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3.] Like the digital root of A000045, sequence is period 24, and likewise, its period also adds up to 117.Peter M. Chema, Apr 28 2016
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
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FORMULA
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G.f.: (1+4*x+5*x^2+9*x^3+5*x^4+5*x^5+x^6+6*x^7+7*x^8+4*x^9+2*x^10+6*x^11+8*x^12+5*x^13+4*x^14+9*x^15+4*x^16+4*x^17+8*x^18+3*x^19+2*x^20+5*x^21+7*x^22+3*x^23)/(1-x^24). - Robert Israel, Apr 28 2016
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MAPLE
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A[0]:= 1: A[1]:= 4:
for i from 2 to 100 do
t:= A[i-2]+A[i-1];
A[i]:=(t + 9*(t mod 10))/10;
od:
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MATHEMATICA
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a[0] = 1; a[1] = 4; a[n_] := a[n] = Total@ IntegerDigits[a[n - 1] + a[n - 2]]; Table[a@ n, {n, 0, 120}] (* Michael De Vlieger, Apr 28 2016 *)
nxt[{a_, b_}]:={b, Total[IntegerDigits[a+b]]}; NestList[nxt, {1, 4}, 100][[All, 1]] (* or *) PadRight[{}, 100, {1, 4, 5, 9, 5, 5, 1, 6, 7, 4, 2, 6, 8, 5, 4, 9, 4, 4, 8, 3, 2, 5, 7, 3}] (* Harvey P. Dale, Apr 27 2018 *)
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PROG
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(PARI) a(n)=n=n%24; my(a=3, b=1); while(n, [a, b]=[b, sumdigits(a+b)]; n--); b \\ Charles R Greathouse IV, Apr 28 2016
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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