A285633 Numbers k such that (16*10^k + 77)/3 is prime.

0, 1, 4, 11, 12, 24, 33, 42, 52, 58, 87, 114, 143, 169, 227, 292, 544, 1341, 1498, 5011, 7295, 14958, 15577, 103127, 107140, 118852, 122871

Offset

1,3

Comments

For k>1, numbers such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 59 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 53w59.

Example

4 is in this sequence because (16*10^4 + 77)/3 = 53359 is prime.
Initial terms and primes associated:
a(1) = 0, 31;
a(2) = 1, 79;
a(3) = 4, 53359;
a(4) = 11, 533333333359;
a(5) = 12, 5333333333359; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# + 77)/3] &]

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A355608 A098060 A268232 * A266281 A154040 A066985

Adjacent sequences: A285630 A285631 A285632 * A285634 A285635 A285636

Keyword

nonn,more,hard

Author

Robert Price, Apr 23 2017

Extensions

a(24)-a(27) from Robert Price, Mar 10 2019

Status

approved