A345307 Nonpalindromic primes whose binary expansion, interpreted as a base-10 number, yields a palindromic prime.

443, 6827, 7607, 19801, 23581, 31183, 85093, 97213, 314777, 364621, 370477, 382813, 450011, 524287, 1077697, 1159601, 1177073, 1215017, 1299833, 1311749, 1356197, 1458253, 1547069, 1589123, 1613987, 1649299, 1716619, 1851271, 1893607, 2092799, 4404833, 4454369, 4671857

Offset

1,1

Links

Table of n, a(n) for n=1..33.

Example

443 is a nonpalindromic prime. Its binary expansion is 110111011, which, when interpreted as a base-10 number, is a palindromic prime.

Mathematica

Select[Range[5000000], PrimeQ[#] && ! PalindromeQ[#] && PrimeQ[FromDigits[IntegerDigits[#, 2]]] && PalindromeQ[FromDigits[IntegerDigits[#, 2]]] &]
ppQ[p_]:=With[{c=FromDigits[IntegerDigits[p, 2], 10]}, PrimeQ[c]&&PalindromeQ[c]]; Select[Prime[ Range[ 330000]], !PalindromeQ[#]&&ppQ[#]&] (* Harvey P. Dale, Feb 11 2024 *)

Prog

(Python)
from sympy import isprime, primerange
def ispal(s): return s == s[::-1]
def aupto(limit):
    alst = []
    for p in primerange(13, limit+1):
        if not ispal(str(p)):
            b = bin(p)[2:]
            if ispal(b) and isprime(int(b)): alst.append(p)
    return alst
print(aupto(5*10**6)) # Michael S. Branicky, Jun 13 2021

Crossrefs

Cf. A002385, A006995.

Sequence in context: A031699 A158321 A293978 * A205604 A205435 A098254

Adjacent sequences: A345304 A345305 A345306 * A345308 A345309 A345310

Keyword

nonn,base

Author

Tanya Khovanova, Jun 13 2021

Status

approved