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).
1, 2, 4, 8, 16, 53, 67, 122, 135, 270, 321, 329, 1065, 1907, 4390, 5132, 5181, 5700, 5754, 6189, 13269, 73632, 73977, 93930, 94758, 128519, 661103, 661876, 729478, 1009425, 1095200, 1096587, 2187425, 2269554, 2311471, 2430158, 4542981, 4864284, 5143384, 5422306
Offset: 1
Examples
a(5)=16, so a(6) is 16 + 1^1 + 6^2 = 53.
Links
- Pieter Post, Table of n, a(n) for n = 1..100
Programs
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Mathematica
NestList[#+Total[IntegerDigits[#]^Range[IntegerLength[#]]]&,1,40] (* Harvey P. Dale, Jan 19 2021 *)
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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 -
Python
def moda(n): return sum(int(d)**(i + 1) for i, d in enumerate(str(n))) b = 1 resu = [1] for a in range(1, 100): b += moda(b) resu.append(b) resu -
Sage
A=[1] for i in [1..2000]: 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])) A # Tom Edgar, Oct 20 2015
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