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A144582
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Numbers having the same leading decimal digit as their cube.
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5
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0, 1, 10, 11, 12, 28, 29, 32, 33, 34, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287
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OFFSET
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1,3
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COMMENTS
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For k > 0, write k = s * 10^t, 1 <= s < 10, then k is a term if and only if s is in [1, 2^(1/3)) U (20^(1/3), 3) U (30^(1/3), 40^(1/3)) U (30^(2/3), 10). - Jianing Song, Dec 26 2022
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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A000030(a(n)) = A002994(a(n)) = A000030(A000578(a(n))).
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EXAMPLE
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a(13)=99 and 970299=99^3 start both with 9.
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MATHEMATICA
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Select[Range[0, 300], First[IntegerDigits[#]]== First[IntegerDigits[#^3]]&] (* Harvey P. Dale, Mar 14 2011 *)
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PROG
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(PARI) isok(n) = (n == 0) || (digits(n)[1] == digits(n^3)[1]); \\ Michel Marcus, Mar 18 2015
(Haskell)
a144582 n = a144582_list !! (n-1)
a144582_list = [x | x <- [0..], a000030 x == a000030 (x ^ 3)]
-- Reinhard Zumkeller, Apr 01 2015
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CROSSREFS
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Cf. A000030, A002994, A000578, A089951, A256523 (subsequence).
Sequence in context: A102695 A252481 A308854 * A048024 A048002 A256523
Adjacent sequences: A144579 A144580 A144581 * A144583 A144584 A144585
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Aug 17 2008
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STATUS
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approved
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