A179622 n such that n is the sum of previous numbers found using n's digits as offsets.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 19, 18, 28, 27, 37, 36, 46, 45, 55, 46, 91, 101, 92, 137, 147, 138, 183, 193, 184, 138, 321, 331, 322, 276, 459, 469, 460, 414, 597, 459, 928, 919, 873, 1056, 918, 1387, 1378, 1332, 1515, 1056, 1974, 2443, 2434

Offset

1,11

Links

Michael S. Branicky, Table of n, a(n) for n = 1..6588

Formula

For n < 10, a(n) = 1.

For n >= 10, a(n) = a(n - first nonzero digit of n) + a(n - second nonzero digit of n) + ... + a(n - last nonzero digit of n).

Example

a(10) = a(10 - 1), nonzero digits in n are skipped.
a(12) = a(12 - 1) + a(12 - 2).
a(312) = a(312 - 3) + a(312 - 1) + a(312 - 2).

Mathematica

a[1] = a[2] = a[3] = a[4] = a[5] = a[6] = a[7] = a[8] = a[9] = 1; a[n_] := Block[{s = Select[ IntegerDigits@ n, # > 0 &]}, Plus @@ (a[n - # ] & /@ s)]; Array[a, 63] (* Robert G. Wilson v, Aug 23 2010 *)

Prog

(Python)
def A179622(up_to_n):
    sequence=[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
    for n in range(len(sequence), up_to_n+1):
        seed_of_new_element=[-int(x) for x in str(n).replace("0", "")]
        new_element=sum(list(map(sequence.__getitem__, seed_of_new_element)))
        sequence.append(new_element)
    return sequence
A179622(63) # Bence Bernáth, Nov 08 2022
(Python)
from functools import cache
@cache
def a(n): return 1 if n<10 else sum(a(n-int(i)) for i in str(n) if i!='0')
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Nov 12 2022

Crossrefs

Sequence in context: A334387 A051503 A331375 * A367617 A367366 A285757

Adjacent sequences: A179619 A179620 A179621 * A179623 A179624 A179625

Keyword

nonn,base

Author

Dominick Cancilla, Jul 20 2010

Status

approved