A397072 a(n) is the first prime p such that the concatenation of the last digits of n consecutive primes starting with p is prime.

2, 2, 5, 2, 31, 13, 17, 5, 7, 43, 41, 13, 2, 37, 23, 2, 2, 101, 47, 7, 11, 17, 5, 331, 31, 7, 23, 2, 349, 79, 67, 139, 271, 2, 281, 31, 97, 37, 383, 239, 263, 127, 137, 157, 97, 593, 11, 167, 113, 389, 449, 307, 179, 617, 199, 349, 127, 127, 131, 7, 397, 317, 179, 577, 1487, 659, 307, 31, 379, 37

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(5) = 31 because the 5 consecutive primes starting with 31 are 31, 37, 41, 43 and 47, the concatenation of their last digits is 17137, which is prime, and no prime less than 31 works.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
lcat:= proc(L) local i, t;
  add((L[i] mod 10)*10^(nops(L)-i), i=1..nops(L))
end proc:
f:= proc(n) local i, j, v;
  for i from 1 do
    v:= lcat(P[i..i+n-1]);
    if isprime(v) then return P[i] fi
  od
end proc:
map(f, [$1..100]);

Mathematica

a[n_]:=Module[{p=0}, Until[PrimeQ[FromDigits[Last/@IntegerDigits/@Prime[Range[p, p+n-1]]]], p++]; Prime[p]]; Array[a, 70] (* James C. McMahon, Jul 05 2026 *)

Prog

(Python)
from itertools import islice
from gmpy2 import mpz, is_prime
from sympy import primerange
def agen(LIM=10**6): # generator of terms, capped by LIM
    primes = list(primerange(1, LIM+1))
    L = [str(p%10) for p in primes] # last digits of primes
    n, an = 1, True
    while an:
        an = next((primes[i] for i in range(len(primes)-n) if is_prime(mpz("".join(L[i:i+n])))), None)
        if an: yield an; n += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Jul 05 2026

Crossrefs

Cf. A007652, A397073.

Sequence in context: A226135 A284464 A038041 * A392900 A392903 A197591

Adjacent sequences: A397068 A397069 A397070 * A397073 A397074 A397075

Keyword

nonn,base,changed

Author

Will Gosnell and Robert Israel, Jun 15 2026

Status

approved