A050814 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.

5333, 1454969, 1466833, 1790531, 1794343, 1883113, 1984459, 2179993, 2410523, 2567891, 3100301, 3259567, 3424783, 3700153, 3954131, 3972979, 4046671, 4134133, 4280033, 4544641, 4691851, 4692641, 4848523, 5006831, 5118307

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Example

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).

Mathematica

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 *)

Crossrefs

Cf. A050674-A050719.

Sequence in context: A031571 A031751 A023342 * A234213 A187435 A023939

Adjacent sequences: A050811 A050812 A050813 * A050815 A050816 A050817

Keyword

nonn,base

Author

Patrick De Geest, Oct 15 1999

Extensions

Offset changed to 1 by Jon E. Schoenfield, Oct 17 2019

Name clarified by Tanya Khovanova, Jul 06 2021

Status

approved