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A263535 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).

%I A263535 #28 Jan 19 2021 18:48:07
%S A263535 1,2,4,8,16,53,67,122,135,270,321,329,1065,1907,4390,5132,5181,5700,
%T A263535 5754,6189,13269,73632,73977,93930,94758,128519,661103,661876,729478,
%U A263535 1009425,1095200,1096587,2187425,2269554,2311471,2430158,4542981,4864284,5143384,5422306
%N A263535 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 A263535 This additive sequence will tend to be geometric.
%H A263535 Pieter Post, <a href="/A263535/b263535.txt">Table of n, a(n) for n = 1..100</a>
%e A263535 a(5)=16, so a(6) is 16 + 1^1 + 6^2 = 53.
%t A263535 NestList[#+Total[IntegerDigits[#]^Range[IntegerLength[#]]]&,1,40] (* _Harvey P. Dale_, Jan 19 2021 *)
%o A263535 (Python)
%o A263535 def moda(n):
%o A263535     return sum(int(d)**(i + 1) for i, d in enumerate(str(n)))
%o A263535 b = 1
%o A263535 resu = [1]
%o A263535 for a in range(1, 100):
%o A263535     b += moda(b)
%o A263535     resu.append(b)
%o A263535 resu
%o A263535 (Sage) A=[1]
%o A263535 for i in [1..2000]:
%o A263535     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 A263535 A # _Tom Edgar_, Oct 20 2015
%o A263535 (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 A263535 Cf. A007629, A005188.
%K A263535 nonn,base
%O A263535 1,2
%A A263535 _Pieter Post_, Oct 20 2015