A360781 - OEIS

%I #19 Feb 24 2023 20:21:41

%S 2,3,5,7,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,101,103,

%T 107,109,113,131,139,149,151,157,163,173,179,191,193,197,211,223,227,

%U 233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331

%N Primes p such that at least one number remains prime when p is bracketed by a single digit d; that is, at least one instance of d//p//d is prime where // means concatenation.

%C The bracketing digit d must be 1, 3, 7, or 9.

%H Michael S. Branicky, <a href="/A360781/b360781.txt">Table of n, a(n) for n = 1..10000</a>

%F Union of A069687, A069688, A069689, A069690. - _Alois P. Heinz_, Feb 22 2023

%e 263 is included because 263 is a prime and 32633 (and also 92639) is a prime.

%p q:= p-> ormap(isprime, map(d-> parse(cat(d, p, d)), [1, 3, 7, 9])):

%p select(q, [ithprime(i)$i=1..67])[];  # _Alois P. Heinz_, Feb 22 2023

%t brkQ[p_]:=AnyTrue[Table[FromDigits[Join[{d},IntegerDigits[p],{d}]],{d,{1,3,7,9}}],PrimeQ]; Select[Prime[Range[100]],brkQ]

%o (Python)

%o from sympy import isprime, nextprime

%o from itertools import islice

%o def agen(): # generator of terms

%o     p = 2

%o     while True:

%o         sp = str(p)

%o         if any(isprime(int(d+sp+d)) for d in "1379"):

%o             yield p

%o         p = nextprime(p)

%o print(list(islice(agen(), 57))) # _Michael S. Branicky_, Feb 20 2023

%o (PARI) is(p) = my(d=digits(p)); forstep(k=1, 9, 2, if (isprime(fromdigits(concat(k, concat(d,k)))), return(1)));

%o isok(p) = if (isprime(p), is(p)); \\ _Michel Marcus_, Feb 20 2023

%Y Cf. A000040, A059694, A069687, A069688, A069689, A069690.

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Feb 20 2023