A347344 - OEIS

%I #32 Oct 02 2021 15:02:39

%S 1,13,23,27,29,31,37,43,49,57,61,73,81,83,87,91,97,103,109,117,123,

%T 129,151,153,163,171,181,187,193,203,207,213,221,237,239,243,251,267,

%U 269,273,281,287,293,297,301,307,313,319,323,329,331,343,347,359,361

%N Positive integers k such that k with the first (most significant) digit repeated is prime.

%C 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.

%H Michael S. Branicky, <a href="/A347344/b347344.txt">Table of n, a(n) for n = 1..10000</a>

%e 27 is a term because 227 is prime.

%t upto=500;Select[Range[1,upto,2],PrimeQ[FromDigits[Join[{First[d=IntegerDigits[#]]},d]]]&]

%o (Python)

%o from sympy import isprime

%o def ok(n): s = str(n); return isprime(int(s[0] + s))

%o print(list(filter(ok, range(362)))) # _Michael S. Branicky_, Aug 27 2021

%o (PARI) isok(k) = my(d=digits(k)); isprime(eval(fromdigits(concat(d[1], d)))); \\ _Michel Marcus_, Sep 09 2021

%Y Cf. A000040, A226099, A347343.

%K nonn,base

%O 1,2

%A _Paolo Xausa_, Aug 27 2021