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A350311
Replace 2^k in the binary expansion of n with A000930(k+2), Narayana's cows sequence.
2
0, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 7, 8, 9, 10, 6, 7, 8, 9, 9, 10, 11, 12, 10, 11, 12, 13, 13, 14, 15, 16, 9, 10, 11, 12, 12, 13, 14, 15, 13, 14, 15, 16, 16, 17, 18, 19, 15, 16, 17, 18, 18, 19, 20, 21, 19, 20, 21, 22, 22, 23, 24, 25, 13, 14, 15, 16, 16, 17
OFFSET
0,3
COMMENTS
A048715(n) = m, if and only if a(n) = m and for all k > n a(k) > m.
MAPLE
b:= (n, i, j, k)->`if`(n=0, 0, k*irem(n, 2, 'q')+b(q, j, k, i+k)):
a:= n-> b(n, 1$3):
seq(a(n), n=0..100); # Alois P. Heinz, Jan 26 2022
PROG
(Python)
def Interpretation(n):
f0, f1, f2, r = 1, 1, 1, 0
while n > 0:
if n%2 == 1:
r = r+f0
n, f0, f1, f2 = n//2, f0+f2, f0, f1
return r
n = 0
while n <= 69:
print(Interpretation(n), end = ", ")
n += 1
(PARI) my(p=Mod('x, 'x^3-'x^2-1)); a(n) = vecsum(Vec(lift(subst(Pol(binary(n))*'x^2, 'x, p)))); \\ Kevin Ryde, Dec 26 2021
CROSSREFS
Cf. A022290 (analog for Fibonacci numbers).
Sequence in context: A202704 A273004 A029931 * A331297 A322806 A332809
KEYWORD
nonn,base
AUTHOR
A.H.M. Smeets, Dec 24 2021
STATUS
approved