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

1,2

Comments

This additive sequence will tend to be geometric.

Links

Pieter Post, Table of n, a(n) for n = 1..100

Example

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

Mathematica

NestList[#+Total[IntegerDigits[#]^Range[IntegerLength[#]]]&, 1, 40] (* Harvey P. Dale, Jan 19 2021 *)

Prog

(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
(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

Crossrefs

Cf. A007629, A005188.

Sequence in context: A264635 A046237 A013084 * A018681 A367172 A018735

Adjacent sequences: A263532 A263533 A263534 * A263536 A263537 A263538

Keyword

nonn,base

Author

Pieter Post, Oct 20 2015

Status

approved