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
Examples
101 is a member since it is a palindromic prime such that 101^2=10201 is a palindrome.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..27
Programs
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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 -
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
Extensions
a(15)-a(19) from Giovanni Resta, May 11 2013
Comments