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 A030139 a(n+1) = sum of digits of (a(n) + a(n-1)). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS 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). FORMULA 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 MAPLE 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: seq(A[i], i=0..100); # Robert Israel, Apr 28 2016 MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A195787 A010667 A016722 * A069228 A200354 A021689 Adjacent sequences:  A030136 A030137 A030138 * A030140 A030141 A030142 KEYWORD nonn,base,easy AUTHOR STATUS approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)