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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 Lars Blomberg, Table of n, a(n) for n = 1..91 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 Adjacent sequences: A256492 A256493 A256494 * A256496 A256497 A256498 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.)