A244442 a(n) is the smallest prime p such that all the n numbers dip(p), dip(dip(p)), ..., dip(dip(...(dip(p))...)) are primes. The function dip is defined in the comment lines.

2, 2, 2, 834007, 53918617, 53918617

Offset

1,1

Comments

dip(m) is the number that is obtained from m by changing each zero digit of m to 1 and each nonzero digit i of m to the i-th prime.

For example dip(103)=2.1.5=215 and dip(19)=2.23=223.

Since each positive integer starts with a nonzero digit, dip is well defined.

Links

Table of n, a(n) for n=1..6.

Example

a(4)=834007 because the four numbers:
1. dip(834007)=19.5.7.1.1.17=19571117,
2. dip(dip(834007)),
3. dip(dip(dip(834007))),
4. dip(dip(dip(dip(834007))))
are all primes and 834007 is the smallest prime with this property.

Crossrefs

Cf. A000040.

Sequence in context: A207820 A186069 A280842 * A338700 A246471 A289814

Adjacent sequences: A244439 A244440 A244441 * A244443 A244444 A244445

Keyword

nonn,base,more,hard

Author

Jahangeer Kholdi and Farideh Firoozbakht, Jul 07 2014

Status

approved