A347343 Positive integers k such that k with the last digit repeated is prime.

1, 19, 21, 23, 27, 31, 43, 49, 57, 59, 67, 73, 81, 87, 91, 97, 103, 127, 139, 143, 149, 151, 169, 173, 177, 181, 187, 193, 199, 201, 209, 211, 231, 233, 237, 239, 241, 247, 263, 267, 269, 271, 277, 283, 299, 301, 329, 343, 349, 351, 353, 367, 373, 383, 387

Offset

1,2

Links

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

Formula

a(n) ~ n log n by the prime number theorem in arithmetic progressions. (These numbers are the primes mod 11, 33, 77, or 99 mod 100 with their last digit removed.) - Charles R Greathouse IV, Aug 27 2021

Example

21 is a term because 211 is prime.

Mathematica

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

Prog

(PARI) forprime(p=9, 1e4, if(p%100%11==0, print1(p\10", "))) \\ Charles R Greathouse IV, Aug 27 2021
(Python)
from sympy import isprime
def ok(n): return isprime(10*n + n%10)
print(list(filter(ok, range(388)))) # Michael S. Branicky, Aug 28 2021

Crossrefs

Cf. A000040, A226099.

Sequence in context: A089837 A020347 A334103 * A054864 A158232 A178889

Adjacent sequences: A347340 A347341 A347342 * A347344 A347345 A347346

Keyword

nonn,base,easy

Author

Paolo Xausa, Aug 27 2021

Status

approved