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A256495 Palindromes i such that 2*i^2 is a palindrome. 1
0, 1, 2, 11, 101, 111, 1001, 1111, 10001, 10101, 11011, 100001, 101101, 110011, 1000001, 1001001, 1010101, 1100011, 10000001, 10011001, 10100101, 11000011, 100000001, 100010001, 100101001, 101000101, 110000011, 1000000001, 1000110001, 1001001001, 1010000101 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Subsequence of palindromes of A256437.
The sequence contains all positive integers of the form: m*10^(i + NumberOfDigit(m)) + m where i is any nonnegative integer and m is any term of A000533.
Also contains 1 + 10^i and 1 + 10^i + 10^(2*i) for all i >= 1. Are there any members with more than four 1's, or any members other than 2 with digits other than 0's and 1's? - Robert Israel, Apr 13 2015
LINKS
EXAMPLE
Palindrome 11 is in the sequence because 2*11^2 = 242, a palindrome.
MAPLE
dmax:= 11: # to get all terms with at most dmax digits
revdigs:= proc(n)
local L, i;
L:= convert(n, base, 10);
add(10^(i-1)*L[-i], i=1..nops(L));
end proc:
filter:= proc(n) local L;
L:= convert(2*n^2, base, 10);
L = ListTools:-Reverse(L)
end proc:
A:= {}:
for d from 1 to dmax do
if d::even then
A:= A union select(filter, {seq(10^(d/2)*x + revdigs(x), x=10^(d/2-1)..10^(d/2)-1)})
else
m:= (d-1)/2;
A:= A union select(filter, {seq(seq(10^(m+1)*x + y*10^m + revdigs(x), y=0..9), x=10^(m-1)..10^m-1)})
fi
od:
A; # if using Maple 11 or earlier, uncomment the next line
# sort(convert(A, list)); # Robert Israel, Apr 13 2015
MATHEMATICA
palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[
Range@ 10000000, palQ@ # && palQ[#^2 + FromDigits[Reverse@ IntegerDigits@ #]^2] &] (* Michael De Vlieger, Mar 31 2015 *)
Select[Range[0, 10101*10^5], AllTrue[{#, 2#^2}, PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 26 2020 *)
PROG
(PARI) ispal(n) = my(d = digits(n)); Vecrev(d) == d;
lista(nn) = {for (n=0, nn, if (ispal(n) && ispal(2*n^2), print1(n, ", ")); ); } \\ Michel Marcus, Mar 31 2015
CROSSREFS
Cf. A256437.
Sequence in context: A263607 A083394 A263611 * A087988 A072382 A038136
KEYWORD
nonn,base
AUTHOR
Bui Quang Tuan, Mar 31 2015
EXTENSIONS
a(19)-a(22) from Michel Marcus, Mar 31 2015
a(23)-a(31) from Lars Blomberg, Apr 13 2015
STATUS
approved

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Last modified June 25 04:03 EDT 2024. Contains 373697 sequences. (Running on oeis4.)