A347343 -id:A347343 - cp's OEIS frontend

A347344 Positive integers k such that k with the first (most significant) digit repeated is prime.

1, 13, 23, 27, 29, 31, 37, 43, 49, 57, 61, 73, 81, 83, 87, 91, 97, 103, 109, 117, 123, 129, 151, 153, 163, 171, 181, 187, 193, 203, 207, 213, 221, 237, 239, 243, 251, 267, 269, 273, 281, 287, 293, 297, 301, 307, 313, 319, 323, 329, 331, 343, 347, 359, 361

Offset: 1

Paolo Xausa, Aug 27 2021

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.

			27 is a term because 227 is prime.

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

Cf. A000040, A226099, A347343.

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

isok(k) = my(d=digits(k)); isprime(eval(fromdigits(concat(d[1], d)))); \\ Michel Marcus, Sep 09 2021

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

cp's OEIS Frontend

A347344 Positive integers k such that k with the first (most significant) digit repeated is prime.

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