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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

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

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Last modified June 25 06:10 EDT 2019. Contains 324347 sequences. (Running on oeis4.)