A237575
Fibonacci-like numbers with nonincreasing positive digits. Let a** denote the number that is obtained from a if its digits are written in nonincreasing order. Let a<+>b = (a + b)**. a(0)=0, a(1)=1, for n>=2, a(n) = a(n-1) <+> a(n-2).
Original entry on oeis.org
0, 1, 1, 2, 3, 5, 8, 31, 93, 421, 541, 962, 5310, 7622, 93221, 843100, 963321, 8642110, 9654310, 98642210, 986522100, 8654311100, 9864332000, 88654311100, 98865431100, 987754221100, 9866652211000, 86544432110000, 98644321110000, 888755322110000
Offset: 0
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a:= proc(n) option remember; `if`(n<2, n, parse(cat(
sort(convert(a(n-1)+a(n-2), base, 10), `>`)[])))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Aug 31 2022
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a[0]:=0;a[1]:=1;a[n_]:=a[n]=FromDigits[Reverse[Sort[IntegerDigits[a[n-1]+a[n-2]]]]];Map[a,Range[0,20]] (* Peter J. C. Moses, Feb 09 2014 *)
A237671
Let m_n denote the number which is obtained from n-base representation of m if its digits are written in nondecreasing order; then a(n) is the smallest period of the sequence which is defined by the recurrence b(0)=0, b(1)=1, b(k)=(b(k-1) + b(k-2))_n, for k>=2, or a(n)=0, if there is no such period.
Original entry on oeis.org
1, 3, 16, 6, 20, 24, 16, 36, 120, 300, 20, 288, 28, 192, 200, 552, 180, 192, 180, 1380, 224, 60, 1728, 912, 3800, 756, 576, 1776, 4102, 15480, 3540, 1344, 10800, 14328, 800, 2304, 1520, 1890, 1232, 11280, 9040, 31152, 49544, 3660, 6360, 3696, 13248, 21408
Offset: 2
For n=5, b-sequence begins 0,1,1,2,3,1,4,1,1,2,... It has period {1,1,2,3,1,4} of length 6. So a(5)=6.
a(10) = 120, because the eventual period of A069638 is 120.
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import sympy,functools
def digits2int(x,b):
return functools.reduce(lambda n,d:b*n+d,x,0)
def A237671(n):
return next(sympy.cycle_length(lambda x:(x[1],digits2int(sorted(sympy.ntheory.factor_.digits(sum(x),n)[1:]),n)),(0,1)))[0] # Pontus von Brömssen, Aug 28 2020
A238019
The first position of the first cycle of sequence {b_k}={b_k}(n) in A237671.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 213, 237, 61, 1, 7534, 289, 328, 107, 1291, 787, 23669, 26237, 1001, 2563, 52781, 101705, 22344, 9952, 68955, 1169, 278, 225448, 187013, 140090, 2785328, 5754090, 622017, 531034, 422605, 857311, 502981, 468270, 855421, 38278372, 1552808
Offset: 2
Showing 1-3 of 3 results.
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