A112395 Next term is the sum of the previous 10 digits in the sequence.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 23, 28, 37, 44, 40, 37, 42, 38, 39, 43, 46, 46, 50, 44, 40, 37, 37, 37, 42, 40, 40, 34, 31, 25, 26, 30, 29, 33, 35, 36, 37, 44, 41, 40, 36, 36, 35, 35, 38, 45, 45, 45, 46, 48, 49, 53, 52, 50, 45, 42, 35, 35, 36, 40, 35, 37, 39, 43, 41

Offset: 1

Author

Eric Angelini, Dec 05 2005

Keywords

• base
• easy
• nonn

Comments

Digits, not terms!

There are only 10^10 possibilities for the last 10 digits, so the sequence must eventually cycle.

Cycles at n(19) = 44 and the loop has 312 terms. - Hans Havermann

Terms computed by Gilles Sadowski.

Examples

			0 + 0 + 1 + 1 + 2 + 4 + 8 + 1 + 6 = 23
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..331 (through first loop)

Programs

Mathematica

a[1] = a[2] = a[3] = a[4] = a[5] = a[6] = a[7] = a[8] = a[9] = 0; a[10] = 1; a[n_] := a[n] = Plus @@ Take[ Flatten@Table[IntegerDigits[a[i]], {i, n - 10, n - 1}], -10]; Array[a, 74] (* Robert G. Wilson v, Dec 09 2005 *)

Python

from itertools import islice
def agen(): # generator of terms
    last10 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
    print(last10[:0])
    yield from last10
    while True:
        an = sum(last10)
        yield an
        d = list(map(int, str(an)))
        last10 = last10[-max(10-len(d), 0):] + d[-min(len(d), 10):]
print(list(islice(agen(), 74))) # Michael S. Branicky, Oct 03 2024