A245878 Primes p such that p - d and p + d are also primes, where d is the smallest nonzero digit of p.

67, 607, 6977, 68897, 69067, 69997, 79867, 80677, 88867, 97967, 609607, 660067, 669667, 676987, 678767, 697687, 707677, 766867, 777677, 786697, 866087, 879667, 880667, 886987, 899687, 906707, 909767, 966997, 990967, 6069977, 6096907, 6097997, 6678877

Offset

1,1

Comments

Intersection of A245744 and A245745.

The smallest nonzero digit of a(n) is 6, and the least significant digit of a(n) is 7.

Links

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

Example

The prime 607 is in the sequence because 607 - 6 = 601 and 607 + 6 = 613 are both primes.

Maple

f:= proc(x) local L, i, y;
   L:= subs(1=6, 2=7, 3=8, 4=9, convert(x, base, 5));
   if not member(6, L) then return NULL fi;
   y:= add(L[i]*10^(i-1), i=1..nops(L));
   if isprime(y) and isprime(y-6) and isprime(y+6) then y else NULL fi
end proc:
map(f, [seq(2+5*k, k=1..10000)]); # Robert Israel, Nov 25 2024

Mathematica

pdQ[p_]:=Module[{c=Min[DeleteCases[IntegerDigits[p], 0]]}, AllTrue[p+{c, -c}, PrimeQ]]; Select[Prime[Range[460000]], pdQ] (* Harvey P. Dale, Feb 26 2023 *)

Prog

(PARI) s=[]; forprime(p=2, 7000000, v=vecsort(digits(p), , 8); d=v[1+!v[1]]; if(isprime(p-d) && isprime(p+d), s=concat(s, p))); s
(Python)
from sympy import isprime
from sympy import prime
for n in range(1, 10**6):
  s=prime(n)
  lst = []
  for i in str(s):
    if i != '0':
      lst.append(int(i))
  if isprime(s+min(lst)) and isprime(s-min(lst)):
    print(s, end=', ')
# Derek Orr, Aug 13 2014

Crossrefs

Cf. A245742, A245743, A245744, A245745, A245877.

Sequence in context: A163150 A120717 A200963 * A289867 A142139 A178004

Adjacent sequences: A245875 A245876 A245877 * A245879 A245880 A245881

Keyword

nonn,base,look

Author

Colin Barker, Aug 05 2014

Status

approved