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 A027829 Palindromic squares with an even number of digits. 4
 698896, 637832238736, 4099923883299904, 6916103777337773016196, 40460195511188111559106404, 4872133543202112023453312784, 9658137819052882509187318569, 46501623417708833880771432610564, 1635977102407987117897042017795361, 163296619873968186681869378916692361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Charles Ashbacher, More on palindromic squares, J. Rec. Math. 22, no. 2 (1990), 133-135. [A scan of the first page of this article is included with the last page of the Keith (1990) scan] LINKS M. F. Hasler, Table of n, a(n) for n = 1..14 K. S. Brown, On General Palindromic Numbers Patrick De Geest, Palindromic Squares Patrick De Geest, Subsets of Palindromic Squares Michael Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132. [Annotated scanned copy] FORMULA a(n) = A016113(n)^2. - M. F. Hasler, Jun 08 2014 EXAMPLE 836^2 = 698896, which is palindromic, so 698896 is in the sequence. 1001^2 = 1002001, which is palindromic, but it has an odd number of digits, so it's not in the sequence. MATHEMATICA Select[Range[1000000]^2, PalindromeQ[#] && OddQ[Floor[Log[10, #]]] &] (* Alonso del Arte, Oct 11 2019 *) PROG (PARI) is_A027829(n)={issquare(n)&&Vecrev(n=digits(n))==n&&!bittest(#n, 0)} \\ This is faster than first checking for even length if applied to numbers known to have an even number of digits, as should be the case for a systematic search. For this, one should only consider squares, i.e., rather use is_A016113. - M. F. Hasler, Jun 08 2014 (Scala) def isPalindromic(n: BigInt): Boolean = n.toString == n.toString.reverse val squares = ((1: BigInt) to (1000000: BigInt)).map(n => n * n) squares.filter(n => isPalindromic(n) && n.toString.length % 2 == 0) // Alonso del Arte, Oct 07 2019 (Python) from math import isqrt from itertools import count, islice def A027829_gen(): # generator of terms return filter(lambda n: (s:=str(n))[:(t:=(len(s)+1)//2)]==s[:-t-1:-1], map(lambda n: n**2, (d for l in count(2, 2) for d in range(isqrt(10**(l-1))+1, isqrt(10**l)+1)))) A027829_list = list(islice(A027829_gen(), 3)) # Chai Wah Wu, Jun 23 2022 CROSSREFS Cf. A002113, A002778, A002779, A016113. Sequence in context: A319917 A205608 A205439 * A258129 A204496 A332850 Adjacent sequences: A027826 A027827 A027828 * A027830 A027831 A027832 KEYWORD nonn,base AUTHOR Keith Devlin, via Boon Leong (boon_leong(AT)hotmail.com) EXTENSIONS Two new terms were recently found by Bennett from UK (communication from Patrick De Geest, Dec. 1999 or before) Edited by M. F. Hasler, Jun 08 2014 STATUS approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)