A085414 -id:A085414 - cp's OEIS frontend

A085412 Numbers n such that concatenation of prime[n] and first digit of prime[n] is prime.

6, 8, 11, 12, 22, 27, 29, 36, 37, 42, 44, 67, 68, 71, 72, 73, 74, 75, 76, 133, 134, 138, 157, 160, 161, 162, 163, 164, 166, 169, 172, 174, 175, 179, 180, 187, 197, 204, 207, 210, 232, 235, 237, 247, 249, 251, 254, 261, 263, 264, 269, 272, 278, 282, 285, 287, 303

Offset: 1

Zak Seidov, Jun 29 2003

			6 is a term because prime[6]=13 and concatenation of 13 and 1 is prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A085413, A085414.

cpfdQ[n_]:=Module[{p=Prime[n]},PrimeQ[10p+IntegerDigits[p][[1]]]]; Select[ Range[ 400],cpfdQ] (* Harvey P. Dale, Apr 06 2017 *)

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

Original entry on oeis.org

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

Zak Seidov, Jun 29 2003

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

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

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

Cf. A085412, A085414.

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

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

Prime[A085412]

cp's OEIS Frontend

A085412 Numbers n such that concatenation of prime[n] and first digit of prime[n] is prime.

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

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