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A075052
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Write down squares and cubes in order, as in A002760. The sequence gives the first differences between terms.
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2
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1, 3, 4, 1, 7, 9, 2, 9, 13, 15, 17, 19, 21, 4, 19, 25, 27, 20, 9, 31, 33, 35, 19, 18, 39, 41, 43, 28, 17, 47, 49, 51, 53, 55, 57, 59, 61, 39, 24, 65, 67, 69, 71, 35, 38, 75, 77, 79, 81, 47, 36, 85, 87, 89, 91, 81, 12, 95, 97, 99, 101, 103, 40, 65, 107, 109, 111, 113, 115, 11
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OFFSET
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1,2
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COMMENTS
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Ordered sequence of squares and cubes is as in A002760.
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LINKS
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FORMULA
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EXAMPLE
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First sorted squares and cubes are: 0, 1, 4, 8, 9, 16, 25, 27, 36, 49, 64, 81, 100, hence a(1) = 1 - 0 = 1, a(10) = 64 - 49 = 15, a(12) = 100 - 81 = 19.
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MATHEMATICA
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Module[{nn=70, sq, cb}, sq=Range[0, nn]^2; cb=Select[Range[nn]^3, #<=sq[[-1]]&]; Join[sq, cb]//Union//Differences] (* Harvey P. Dale, Jun 11 2024 *)
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PROG
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(PARI) lista(nn) = {vec = vector(nn, i, i-1); pp = select(i->(issquare(i) || (ispower(i, 3))), vec); for (i=1, #pp-1, print1(pp[i+1] - pp[i], ", "); ); } \\ Michel Marcus, Oct 03 2013
(Python)
from math import isqrt
from sympy import integer_nthroot
def f(x): return n-1+x+integer_nthroot(x, 6)[0]-(b:=integer_nthroot(x, 3)[0])-(a:=isqrt(x)), a, b
m = n-1
k, a, b = f(n-1)
while m != k:
m = k
k, a, b = f(k)
return min((a+1)**2, (b+1)**3)-m # Chai Wah Wu, Aug 09 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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