A263535 - OEIS

%I #28 Jan 19 2021 18:48:07

%S 1,2,4,8,16,53,67,122,135,270,321,329,1065,1907,4390,5132,5181,5700,

%T 5754,6189,13269,73632,73977,93930,94758,128519,661103,661876,729478,

%U 1009425,1095200,1096587,2187425,2269554,2311471,2430158,4542981,4864284,5143384,5422306

%N a(1) = 1; thereafter a(n) = a(n-1) + d_1^1 + d_2^2 + d_3^3 + ..., where d_1 d_2 d_3 ... is the decimal expansion of a(n-1).

%C This additive sequence will tend to be geometric.

%H Pieter Post, <a href="/A263535/b263535.txt">Table of n, a(n) for n = 1..100</a>

%e a(5)=16, so a(6) is 16 + 1^1 + 6^2 = 53.

%t NestList[#+Total[IntegerDigits[#]^Range[IntegerLength[#]]]&,1,40] (* _Harvey P. Dale_, Jan 19 2021 *)

%o (Python)

%o def moda(n):

%o     return sum(int(d)**(i + 1) for i, d in enumerate(str(n)))

%o b = 1

%o resu = [1]

%o for a in range(1, 100):

%o     b += moda(b)

%o     resu.append(b)

%o resu

%o (Sage) A=[1]

%o for i in [1..2000]:

%o     A.append(A[i-1]+sum(A[i-1].digits()[len(A[i-1].digits())-1-j]^(j+1) for j in [0..len(A[i-1].digits())-1]))

%o A # _Tom Edgar_, Oct 20 2015

%o (PARI) lista(nn) = {print1(a=1, ", "); for (n=2, nn, d = digits(a); na = a + sum(i=1, #d, d[i]^i); print1(na, ", "); a = na;);} \\ _Michel Marcus_, Nov 20 2015

%Y Cf. A007629, A005188.

%K nonn,base

%O 1,2

%A _Pieter Post_, Oct 20 2015