OFFSET
1,2
COMMENTS
Conjecture: the sequence contains infinitely many twin prime pairs (k, k+2) such that (D(k), D(k+2)) is a twin prime pair, where D(x) = x with the most significant digit repeated. The first such k is 659: both (659, 661) and (6659, 6661) are twin prime pairs. All these k begin with either 3, 6, or 9.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
EXAMPLE
27 is a term because 227 is prime.
MATHEMATICA
upto=500; Select[Range[1, upto, 2], PrimeQ[FromDigits[Join[{First[d=IntegerDigits[#]]}, d]]]&]
PROG
(Python)
from sympy import isprime
def ok(n): s = str(n); return isprime(int(s[0] + s))
print(list(filter(ok, range(362)))) # Michael S. Branicky, Aug 27 2021
(PARI) isok(k) = my(d=digits(k)); isprime(eval(fromdigits(concat(d[1], d)))); \\ Michel Marcus, Sep 09 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo Xausa, Aug 27 2021
STATUS
approved