OFFSET

1,3

COMMENTS

a(n) is the smallest f(n) such that f(1)=f(2)=1 and f(i) = OpNoz_i(f(i-1)+f(i-2)) for 2<i<=n, where OpNoz_i is a function that either removes zero digits or keeps the value unchanged (the choice is made for each value of i).

LINKS

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

FORMULA

EXAMPLE

a(23) = 1657 via the path: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 1946, 8711, 1657.

PROG

(Python)

def a(n):

reach = {(1, 1)}

for _ in range(n-1):

newreach = set()

for a, b in reach:

newreach.update([(b, a+b), (b, int(str(a+b).replace('0', '')))])

reach = newreach

return min(reach, key = lambda k:k[0])[0]

CROSSREFS

KEYWORD

nonn,base,easy

AUTHOR

Bryle Morga, Jul 02 2024

STATUS

approved