A225603 Palindromic primes whose square is also a palindrome.

2, 3, 11, 101, 100111001, 110111011, 111010111, 1100011100011, 1100101010011, 1101010101011, 100110101011001, 101000010000101, 101011000110101, 101110000011101, 10000010101000001, 10011010001011001, 10100110001100101, 10110010001001101, 10111000000011101

Offset

1,1

Comments

Subsets of A002385, A057135 and A065378.

Palindromes in A161721. Conjecture: a(n) for n >=3 consists only of the digits 0,1. - Chai Wah Wu, Jan 06 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..27

Example

101 is a member since it is a palindromic prime such that 101^2=10201 is a palindrome.

Mathematica

palQ[n_]:=FromDigits[Reverse[IntegerDigits[n]]]==n; t={}; Do[If[palQ[p=Prime[n]] && palQ[p^2], AppendTo[t, p]], {n, 10^7}]; t

Prog

(Python)
from __future__ import division
from sympy import isprime
def paloddgenrange(t, l, b=10): # generator of odd-length palindromes in base b of 2*t <=length <= 2*l
....if t == 0:
........yield 0
....else:
........for x in range(t+1, l+1):
............n = b**(x-1)
............n2 = n*b
............for y in range(n, n2):
................k, m = y//b, 0
................while k >= b:
....................k, r = divmod(k, b)
....................m = b*m + r
................yield y*n + b*m + k
A225603_list = [2, 3, 11]
for i in paloddgenrange(1, 10):
....s = str(i*i)
....if s == s[::-1] and isprime(i):
........A225603_list.append(i) # Chai Wah Wu, Jan 06 2015

Crossrefs

Cf. A002385, A057135, A065378.

Sequence in context: A117699 A065378 A161721 * A292710 A300898 A079853

Adjacent sequences: A225600 A225601 A225602 * A225604 A225605 A225606

Keyword

nonn,base

Author

Jayanta Basu, May 11 2013

Extensions

a(15)-a(19) from Giovanni Resta, May 11 2013

Status

approved