A295325 Numbers k such that 15*10^k + 1 is prime.

1, 4, 7, 8, 18, 19, 73, 143, 192, 408, 533, 792, 3179, 7709, 9554, 35598, 41587, 52919, 56021, 61604, 78672, 81624

Offset

1,2

Comments

For k > 1, numbers such that the digits 15 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(23) > 10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 150w1

Example

4 is in this sequence because 15*10^4 + 1 = 150001 is prime.
Initial terms and primes associated:
a(1) = 1, 151;
a(2) = 4, 150001;
a(3) = 7, 150000001;
a(4) = 8, 1500000001;
a(5) = 18, 15000000000000000001; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[15*10^# + 1] &]

Prog

(PARI) isok(k) = isprime(15*10^k + 1); \\ Michel Marcus, Nov 20 2017

Crossrefs

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

Sequence in context: A291750 A007285 A225430 * A239290 A057464 A344781

Adjacent sequences: A295322 A295323 A295324 * A295326 A295327 A295328

Keyword

nonn,more,hard

Author

Robert Price, Nov 19 2017

Status

approved