A164329 Numbers which yield a prime whenever a zero is inserted between any two digits.

11, 13, 17, 19, 37, 41, 49, 53, 59, 61, 67, 71, 79, 89, 97, 109, 113, 119, 121, 131, 133, 149, 161, 169, 191, 197, 203, 227, 239, 253, 269, 281, 283, 299, 301, 319, 323, 337, 367, 379, 383, 401, 403, 407, 421, 449, 457, 473, 493, 499, 503, 509, 511, 539, 551

Offset: 1

Author

Farideh Firoozbakht, Sep 22 2009

Keywords

• base
• easy
• nonn

Comments

Single-digit numbers 0, ..., 9 seem to be excluded but would satisfy the condition voidly. - M. F. Hasler, May 10 2018

Examples

			998471 is in the sequence because all the five numbers 9098471, 9908471, 9980471, 9984071 and 9984701 are primes.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A216169 (subset of composite terms), A215417 (subset of primes), A159236 (0 is inserted between all digits).

Cf. A068679 (1 is prefixed, appended or inserted anywhere), A069246 (primes among these), A068673 (1 is prefixed, or appended).

Cf. A158594 (3 is prefixed, appended or inserted anywhere), A215419 (primes among these).

Cf. A069832 (7 is prefixed, appended or inserted anywhere), A215420 (primes among these), A068677 (7 is prefixed or appended).

Cf. A069833 (9 is prefixed, appended or inserted anywhere), A215421 (primes among these).

Cf. A158232 (13 is prefixed or appended).

Programs

Mathematica

f[n_]:=(r=IntegerDigits[n];l=Length[r];For[k=2,PrimeQ[FromDigits[Insert
[r,0,k]]],k++ ];If[k==l+1,n,0]);Select[Range[11,560],f[ # ]>0&]

PARI

is(n, L=logint(n+!n, 10)+1, P)={!for(k=1, L-1, isprime([10*P=10^(L-k),1]*divrem(n, P))||return) && n>9} \\ M. F. Hasler, May 10 2018

Extensions

Erroneous comment and cross-references deleted by M. F. Hasler, May 10 2018