

A335271


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


1



131, 173, 179, 191, 197, 283, 293, 367, 383, 401, 547, 587, 641, 701, 709, 757, 797, 827, 12197, 12289, 53881, 54779, 68927
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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 K1.
If it exists, the next term is > 2^32.


LINKS

Table of n, a(n) for n=1..23.


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, d1, 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


STATUS

approved



