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A225603 Palindromic primes whose square is also a palindrome. 2
2, 3, 11, 101, 100111001, 110111011, 111010111, 1100011100011, 1100101010011, 1101010101011, 100110101011001, 101000010000101, 101011000110101, 101110000011101, 10000010101000001, 10011010001011001, 10100110001100101, 10110010001001101, 10111000000011101 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A117699 A065378 A161721 * A292710 A300898 A079853
KEYWORD
nonn,base
AUTHOR
Jayanta Basu, May 11 2013
EXTENSIONS
a(15)-a(19) from Giovanni Resta, May 11 2013
STATUS
approved

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Last modified June 17 00:51 EDT 2024. Contains 373432 sequences. (Running on oeis4.)