0,1

Each term is created by calculating the sum of the digits of the previous number, and the product of its digits. The results are concatenated to give the new number. Starting with 8, the second number is 88. The third number is generated as follows: 8+8 = 16, 8*8 = 64, which gives 1664. Continuing this way, the 7th number in this sequence becomes 88, equal to the second number of the sequence. Therefore, the pattern 88, 1664, 17144, 17112, 1214, ... repeats indefinitely.

Peter Kagey, Table of n, a(n) for n = 0..9999

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

NestList[FromDigits@ Join[IntegerDigits@ Total@ #, IntegerDigits[Times @@ #]] &@ IntegerDigits@ # &, 8, 48] (* Michael De Vlieger, Aug 26 2016 *)

PadRight[{8}, 50, {1214, 88, 1664, 17144, 17112}] (* Harvey P. Dale, Oct 04 2017 *)

(Haskell)

a271268 = 8 : cycle [88, 1664, 17144, 17112, 1214]

-- Correction by Peter Kagey, Aug 25 2016

(Python)

from functools import reduce

from operator import mul

def product(seq):

return reduce(mul, seq, 1)

def conversion(n):

n = str(n)

return str(sum(int(i) for i in n)) + \

str(product(int(i) for i in n))

def a271268(n):

if n == 1:

return 8

else:

r = 8

while n > 1:

r = conversion(r)

n -= 1

return int(r)

(Python)

from math import prod # first program for illustration - better use the second one

def A271268_gen(n = 8): # optional parameter defines starting value

while True: yield n; d=list(map(int, str(n))); n=int(f"{sum(d)}{prod(d)}")

def A271268(n = None): # if no n given, generator of "infinite" sequence

return (8, 17112, 1214, 88, 1664, 17144)[n%5+1 if n>1 else 0] if n \

else (A271268(n)for n in range(1, 1<<59)) # M. F. Hasler, Apr 01 2025

(PARI) /* first rather for illustration, second is more efficient to get a(n) */

A271268_first(n)=vector(n, i, n=if(i>1, eval(Str(vecsum(n=digits(n)), vecprod(n))), 8))

apply( {A271268(n)=[8, 17112, 1214, 88, 1664, 17144][n%5+(n>1)*2]}, [1..15]) \\ M. F. Hasler, Apr 01 2025

Cf. A271220.

Sequence in context: A378685 A003497 A051605 * A006750 A082783 A137144

Adjacent sequences: A271265 A271266 A271267 * A271269 A271270 A271271

nonn,easy,base

Sander Claassen, Apr 03 2016

Offset changed to 0 by Sean A. Irvine, Apr 12 2025

approved