A335271 Full autoinsertable primes are such primes that remain prime after all the possible internal autoinsertions, one at a time.

131, 173, 179, 191, 197, 283, 293, 367, 383, 401, 547, 587, 641, 701, 709, 757, 797, 827, 12197, 12289, 53881, 54779, 68927, 37898818253

Offset

1,1

Comments

Supposed to have only a finite quantity of terms. If the prime has K digits all the possible internal autoinsertions are K-1.

If it exists, the next term is > 2^32.

Links

Table of n, a(n) for n=1..24.

Example

The prime 131 can be inserted into itself in two positions: 1'131'31, 13'131'1. Both are primes.
The prime 68927 can be inserted into itself in four positions: 6'68927'8927, 68'68927'927, 689'68927'27, 6892'68927'7. All the four are primes.

Prog

(PARI) forprime(p=11, 10^8, my(v=digits(p), d=#v, f=1); for(i=1, d-1, my(t=concat(concat(v[1..i], v), v[i+1..d]), q=fromdigits(t)); if(!isprime(q), f=0; break)); if(f, print1(p, ", "))) \\ Hugo Pfoertner, May 30 2020

Crossrefs

Cf. A247098.

Sequence in context: A345774 A132254 A087832 * A140623 A050261 A180544

Adjacent sequences: A335268 A335269 A335270 * A335272 A335273 A335274

Keyword

nonn,base,more

Author

Carlos Rivera, May 29 2020

Extensions

a(24) from Michael S. Branicky, Mar 27 2023

Status

approved