%I #15 Nov 26 2024 02:17:11
%S 67,607,6977,68897,69067,69997,79867,80677,88867,97967,609607,660067,
%T 669667,676987,678767,697687,707677,766867,777677,786697,866087,
%U 879667,880667,886987,899687,906707,909767,966997,990967,6069977,6096907,6097997,6678877
%N Primes p such that p - d and p + d are also primes, where d is the smallest nonzero digit of p.
%C Intersection of A245744 and A245745.
%C The smallest nonzero digit of a(n) is 6, and the least significant digit of a(n) is 7.
%H Robert Israel, <a href="/A245878/b245878.txt">Table of n, a(n) for n = 1..10000</a>
%e The prime 607 is in the sequence because 607 - 6 = 601 and 607 + 6 = 613 are both primes.
%p f:= proc(x) local L,i,y;
%p L:= subs(1=6,2=7,3=8,4=9, convert(x,base,5));
%p if not member(6,L) then return NULL fi;
%p y:= add(L[i]*10^(i-1),i=1..nops(L));
%p if isprime(y) and isprime(y-6) and isprime(y+6) then y else NULL fi
%p end proc:
%p map(f, [seq(2+5*k,k=1..10000)]); # _Robert Israel_, Nov 25 2024
%t 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 *)
%o (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
%o (Python)
%o from sympy import isprime
%o from sympy import prime
%o for n in range(1, 10**6):
%o s=prime(n)
%o lst = []
%o for i in str(s):
%o if i != '0':
%o lst.append(int(i))
%o if isprime(s+min(lst)) and isprime(s-min(lst)):
%o print(s, end=', ')
%o # _Derek Orr_, Aug 13 2014
%Y Cf. A245742, A245743, A245744, A245745, A245877.
%K nonn,base,look
%O 1,1
%A _Colin Barker_, Aug 05 2014