A018834 Numbers k such that the decimal expansion of k^2 contains k as a substring.

0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 250, 376, 500, 600, 625, 760, 1000, 2500, 3760, 3792, 5000, 6000, 6250, 7600, 9376, 10000, 14651, 25000, 37600, 50000, 60000, 62500, 76000, 90625, 93760, 100000, 109376, 250000, 376000, 495475, 500000, 505025

Offset

1,3

Links

Giovanni Resta, Table of n, a(n) for n = 1..200 (first 126 terms from David W. Wilson)

Example

25^2 = 625 which contains 25.
3792^2 = 14_3792_64, 14651^2 = 2_14651_801.

Mathematica

Select[Range[510000], MemberQ[FromDigits /@ Partition[IntegerDigits[#^2], IntegerLength[#], 1], #] &] (* Jayanta Basu, Jun 29 2013 *)
Select[Range[0, 510000], StringPosition[ToString[#^2], ToString[#]]!={}&] (* Ivan N. Ianakiev, Oct 02 2016 *)

Prog

(Haskell)
import Data.List (isInfixOf)
a018834 n = a018834_list !! (n-1)
a018834_list = filter (\x -> show x `isInfixOf` show (x^2)) [0..]
-- Reinhard Zumkeller, Jul 27 2011
(Python)
from itertools import count, islice
def A018834_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:str(n) in str(n**2), count(max(startvalue, 0)))
A018834_list = list(islice(A018834_gen(), 20)) # Chai Wah Wu, Apr 04 2023

Crossrefs

Cf. A003226, A046831, A046851, A045953.

Cf. A000290. Supersequence of A029943.

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9).

Cf. A029942 (cubes), A075904 (4th powers), A075905 (5th powers).

Sequence in context: A035282 A075156 A075904 * A029943 A356760 A063630

Adjacent sequences: A018831 A018832 A018833 * A018835 A018836 A018837

Keyword

nonn,base

Author

David W. Wilson

Status

approved