A065076 - OEIS

%I #20 Jun 18 2018 03:41:33

%S 0,1,1,2,3,5,8,13,12,16,19,26,27,35,35,43,42,49,55,59,69,74,80,82,90,

%T 91,100,92,111,95,125,103,129,115,136,125,144,134,152,142,159,157,172,

%U 167,186,182,197,199,216,208,226,218,237,230,242,238,255,250,262,260,270

%N a(0) = 0, a(1) = 1, a(n) = (sum of digits of a(n-1)) + a(n-2).

%H Harry J. Smith, <a href="/A065076/b065076.txt">Table of n, a(n) for n = 0..1000</a>

%e a(8) = 12 because a(7) = 13, a(6) = 8 and 4 = 1+3 and 12 = 4 + 8.

%t a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 1] ]] + a[n - 2]; Table[ a[n], {n, 0, 100} ]

%t Transpose[NestList[{Last[#],Total[IntegerDigits[Last[#]]]+First[#]}&, {0,1}, 60]][[1]] (* _Harvey P. Dale_, Dec 07 2011 *)

%o (PARI): digitsum(n) = local(v,d); v=[]; while(n>0,d=divrem(n,10); n=d[1]; v= concat(v,d[2])); sum(j=1,matsize(v)[2],v[j]) a065076(m)=local(a,j,v,w); w=1; print1(w,","); v=1; print1(v,","); for(j=3,m,a=digitsum(v)+w; print1(a,","); w=v; v=a) a065076(65)

%o (PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } { for (n=0, 1000, if (n>1, a=SumD(a1) + a2; a2=a1; a1=a, if (n, a=a1=1, a=a2=0)); write("b065076.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 06 2009

%o (Haskell)

%o a065076 n = a065076_list !! n

%o a065076_list = 0 : 1 : zipWith (+)

%o                 a065076_list (map a007953 $ tail a065076_list)

%o -- _Reinhard Zumkeller_, Nov 13 2014

%Y Cf. A007953 and A007612.

%Y Cf. A030132.

%K nonn,base,easy

%O 0,4

%A _Bodo Zinser_, Nov 09 2001

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Robert G. Wilson v_, Nov 13 2001