A245877 Primes p such that p - d and p + d are also primes, where d is the largest digit of p.

263, 563, 613, 653, 1613, 1663, 3463, 4643, 5563, 5653, 6263, 6323, 12653, 13463, 14633, 16063, 16223, 21163, 21563, 25463, 26113, 30643, 32063, 33623, 36313, 41263, 41603, 44263, 53623, 54623, 56003, 60133, 61553, 62213, 62633, 64013, 65413, 105613, 106213

Offset: 1

Author

Colin Barker, Aug 05 2014

Keywords

• nonn
• base

Comments

Intersection of A245742 and A245743.

The largest digit of a(n) is 6, and the least significant digit of a(n) is 3.

Intersection of A006489, A011536, and complements of A011537, A011538, A011539. - Robert Israel, Aug 05 2014

Examples

			The prime 263 is in the sequence because 263 - 6 = 257 and 263 + 6 = 269 are both primes.
		

Links

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

Crossrefs

Cf. A006489, A245742, A245743, A245744, A245745, A245878.

Programs

Mathematica

pdpQ[n_]:=Module[{m=Max[IntegerDigits[n]]},AllTrue[n+{m,-m},PrimeQ]]; Select[ Prime[Range[11000]],pdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2017 *)

PARI

select(p->d=vecsort(digits(p),,4)[1]; isprime(p-d) && isprime(p+d), primes(20000))

Python

import sympy
from sympy import prime
from sympy import isprime
for n in range(1,10**5):
  s=prime(n)
  lst = []
  for i in str(s):
    lst.append(int(i))
  if isprime(s+max(lst)) and isprime(s-max(lst)):
    print(s,end=', ')
# Derek Orr, Aug 13 2014