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

1,12

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A058961 A130917 A007612 * A004207 A219675 A062729

Adjacent sequences: A112392 A112393 A112394 * A112396 A112397 A112398

Keyword

base,easy,nonn

Author

Eric Angelini, Dec 05 2005

Status

approved