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