A319017 Prime numbers which satisfy the regex m1{1,m1}m2{1,m2}m3{1,m3}m4{1,m4}m5{1,m5} where mi are one-digit Lucas numbers.

21347, 2213347, 2213447, 21334447, 21344447, 21344777, 22133477, 213334477, 221344477, 2134444777, 22133344447, 221344477777, 2133344447777, 2133347777777, 2213447777777, 22133344447777, 213344447777777, 221333447777777, 22133344447777777

Offset

1,1

Comments

mi=Lucas numbers sequence(i), i.e., m1=2, m2=1, m3=3 and so on.

There are 168 = 2*1*3*4*7 numbers matching this regular expression, of which 19 are prime. - Charles R Greathouse IV, Jan 21 2025

Links

Table of n, a(n) for n=1..19.

Example

The prime number 2213447 belongs to this sequence as 2, 1, 3, 4 and 7 are the one-digit Lucas numbers (ordered as in Lucas number sequence) and each digit k is repeated at most k times (including itself), in accordance with the regex described in the sequence name (2 repeated two times, 1 one time, 3 repeated one time, 4 repeated two times and 7 one time).
The prime number 22133344447777777 is the best example, as each one-digit Lucas number k is repeated exactly k times.

Crossrefs

Subsequence of A178550.

Cf. A000032.

Sequence in context: A349508 A250532 A234454 * A286635 A324259 A083361

Adjacent sequences: A319014 A319015 A319016 * A319018 A319019 A319020

Keyword

nonn,base,fini,full

Author

Pierandrea Formusa, Sep 07 2018

Status

approved