A085413 Prime such that concatenation of it and its first digit is prime.

13, 19, 31, 37, 79, 103, 109, 151, 157, 181, 193, 331, 337, 353, 359, 367, 373, 379, 383, 751, 757, 787, 919, 941, 947, 953, 967, 971, 983, 1009, 1021, 1033, 1039, 1063, 1069, 1117, 1201, 1249, 1279, 1291, 1459, 1483, 1489, 1567, 1579, 1597, 1609, 1663, 1669

Offset

1,1

Comments

Indices of primes in A085412; primes as concatenation of prime and its first digit in A085414.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Prime[A085412]

Example

13 is a term because concatenation of 13 and 1 is prime.

Maple

R:= NULL: count:= 0:
for d from 1 while count < 100 do
  for a in [1, 3, 7, 9] do
    for x from 1 to 10^d-1 by 2 while count < 100 do
      if isprime(a*10^d + x) and isprime(a*10^(d+1)+10*x+a) then
        R:= R, a*10^d+x; count:= count+1
fi od od od:
R; # Robert Israel, Mar 24 2023

Prog

(Python)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
    for d in count(1):
        for f in [1, 3, 7, 9]:
            for p in primerange(f*10**d, (f+1)*10**d):
                if isprime(10*p+f):
                    yield p
print(list(islice(agen(), 50))) # Michael S. Branicky, Mar 24 2023

Crossrefs

Cf. A085412, A085414.

Sequence in context: A040092 A079130 A243587 * A342943 A244311 A358530

Adjacent sequences: A085410 A085411 A085412 * A085414 A085415 A085416

Keyword

nonn,base

Author

Zak Seidov, Jun 29 2003

Status

approved