A235000 Primes which become palindromic primes when the digits are rotated once to the right.

2, 3, 5, 7, 11, 199, 277, 311, 577, 733, 811, 877, 911, 977, 10133, 13177, 22277, 27211, 27277, 28211, 32377, 33311, 40499, 43411, 43499, 45433, 46499, 49499, 55511, 60611, 62633, 63611, 65633, 67699, 72733, 79777, 80833, 84811, 87833, 87877, 93911, 98911

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

The prime 277 is in the sequence because 727 is a palindromic prime.

Prog

(PARI) rotr(a) = if(a<10, a, eval(Str(a%10, a\10)))
revint(n) = my(m=n%10); n\=10; while(n>0, m=m*10+n%10; n\=10); m
s=[]; forprime(n=2, 1000000, r=rotr(n); if(isprime(r) && revint(r)==r, s=concat(s, n))); s
(Python)
from sympy import isprime
def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l
....if l > 0:
........yield 0
........for x in range(1, l+1):
............for y in range(10**(x-1), 10**x):
................s = str(y)
................yield int(s+s[-2::-1])
............for y in range(10**(x-1), 10**x):
................s = str(y)
................yield int(s+s[::-1])
A235000_list = []
for x in palQgen10(5):
....s = str(x)
....y = int(s[1:]+s[0])
....if (s[1] if len(s) > 1 else []) != '0' and isprime(x) and isprime(y):
........A235000_list.append(y)
A235000_list = sorted(A235000_list) # Chai Wah Wu, Dec 21 2014

Crossrefs

Cf. A234912.

Sequence in context: A241724 A186449 A046480 * A067906 A029980 A046481

Adjacent sequences: A234997 A234998 A234999 * A235001 A235002 A235003

Keyword

nonn,base,less

Author

Colin Barker, Jan 02 2014

Status

approved