A088136 Primes such that sum of first and last digits is prime.

11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 131, 151, 181, 191, 211, 223, 229, 233, 239, 241, 251, 263, 269, 271, 281, 283, 293, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 601, 607, 617, 631, 641, 647, 661, 677, 691

Offset: 1

Author

Zak Seidov, Sep 20 2003

Keywords

• easy
• nonn
• base

Links

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

Crossrefs

Cf. A008040 (primes), A010051 (isprime), A000030 (first digit of n), A010879 (last digit of n).

Cf. A046704, A007953, A088133, A088134, A088135.

Programs

Mathematica

Select[Prime[Range[400]],PrimeQ[First[IntegerDigits[#]]+ Last[ IntegerDigits[ #]]]&] (* Harvey P. Dale, Jun 23 2017 *)

PARI

select( {is_A088136(p)=isprime(p\10^logint(p,10)+p%10)&&isprime(p)}, primes(99)) \\ M. F. Hasler, Apr 23 2024

Python

from sympy import isprime, primerange
def ok(p): s = str(p); return isprime(int(s[0]) + int(s[-1]))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(691)) # Michael S. Branicky, Nov 23 2021