|
%I #18 Jul 10 2021 00:17:06
%S 5333,1454969,1466833,1790531,1794343,1883113,1984459,2179993,2410523,
%T 2567891,3100301,3259567,3424783,3700153,3954131,3972979,4046671,
%U 4134133,4280033,4544641,4691851,4692641,4848523,5006831,5118307
%N Primes p such that inserting any even digit between adjacent digits produces a prime number while inserting any odd digit produces a composite number, or vice versa.
%e 5333 produces five primes when an even digit is inserted (5030303, 5232323, 5434343, 5636363, 5838383) and five composites when an odd digit is inserted (5131313, 5333333, 5535353, 5737373, 5939393).
%t a[n_,k_]:=Union[Boole/@PrimeQ[Table[FromDigits[Riffle[IntegerDigits[n],i]],{i,k+2*Range[0,4]}]]]; t={}; Do[p=Prime[i]; x=a[p,1]; y=a[p,0]; If[x=={0}&&y=={1}||x=={1}&&y=={0},AppendTo[t,p]],{i,100,190000}]; t (* _Jayanta Basu_, Jun 01 2013 *)
%Y Cf. A050674-A050719.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Oct 15 1999
%E Offset changed to 1 by _Jon E. Schoenfield_, Oct 17 2019
%E Name clarified by _Tanya Khovanova_, Jul 06 2021
|
