A360781 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.

2, 3, 5, 7, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 101, 103, 107, 109, 113, 131, 139, 149, 151, 157, 163, 173, 179, 191, 193, 197, 211, 223, 227, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331

Offset

1,1

Comments

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

Union of A069687, A069688, A069689, A069690. - Alois P. Heinz, Feb 22 2023

Example

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

Maple

q:= p-> ormap(isprime, map(d-> parse(cat(d, p, d)), [1, 3, 7, 9])):
select(q, [ithprime(i)$i=1..67])[];  # Alois P. Heinz, Feb 22 2023

Mathematica

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

Prog

(Python)
from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
    p = 2
    while True:
        sp = str(p)
        if any(isprime(int(d+sp+d)) for d in "1379"):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 57))) # Michael S. Branicky, Feb 20 2023
(PARI) is(p) = my(d=digits(p)); forstep(k=1, 9, 2, if (isprime(fromdigits(concat(k, concat(d, k)))), return(1)));
isok(p) = if (isprime(p), is(p)); \\ Michel Marcus, Feb 20 2023

Crossrefs

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

Sequence in context: A358047 A072885 A178209 * A042994 A129692 A272441

Adjacent sequences: A360778 A360779 A360780 * A360782 A360783 A360784

Keyword

nonn,base

Author

Harvey P. Dale, Feb 20 2023

Status

approved