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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A288502 A320710 A142754 * A142379 A128654 A236245

Adjacent sequences: A245874 A245875 A245876 * A245878 A245879 A245880

Keyword

nonn,base

Author

Colin Barker, Aug 05 2014

Status

approved