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

1,1

Comments

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

Links

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

Example

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

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&]

Prog

(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

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).

Sequence in context: A076162 A156902 A050674 * A159236 A215417 A249376

Adjacent sequences: A164326 A164327 A164328 * A164330 A164331 A164332

Keyword

base,easy,nonn

Author

Farideh Firoozbakht, Sep 22 2009

Extensions

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

Status

approved