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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 *)

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 July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)