The On-Line Encyclopedia of Integer Sequences (OEIS)

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A290150

Numbers k such that (316*10^k - 1)/9 is prime.
(history; published version)

#11 by Michael De Vlieger at Sat Jun 08 15:47:53 EDT 2024

STATUS

proposed

approved

#10 by Jon E. Schoenfield at Sat Jun 08 15:47:25 EDT 2024

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Sat Jun 08 15:47:23 EDT 2024

COMMENTS

Numbers k such that the digits 35 followed by k occurrences of the digit 1 is prime (see Example section).

LINKS

Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficultyprime_difficulty.txt">Search for 351w</a>.

EXAMPLE

Initial terms and primes associated primes:

STATUS

approved

editing

#8 by Susanna Cuyler at Fri Jan 31 20:08:50 EST 2020

STATUS

proposed

approved

#7 by Robert Price at Fri Jan 31 20:08:04 EST 2020

STATUS

editing

proposed

#6 by Robert Price at Fri Jan 31 20:08:01 EST 2020

COMMENTS

a(21) > 2*10^5.

LINKS

Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficulty.txt">Search for 351w.</a>.

STATUS

approved

editing

#5 by Charles R Greathouse IV at Thu Jan 17 13:44:09 EST 2019

LINKS

Makoto Kamada, <a href="httphttps://stdkmd.comnet/nrr">Factorization of near-repdigit-related numbers</a>.

Makoto Kamada, <a href="httphttps://stdkmd.comnet/nrr/prime/primedifficulty.txt">Search for 351w.</a>

Discussion

Thu Jan 17

13:44

OEIS Server: https://oeis.org/edit/global/2791

#4 by N. J. A. Sloane at Sat Jul 22 10:09:40 EDT 2017

STATUS

proposed

approved

#3 by Robert Price at Fri Jul 21 16:44:41 EDT 2017

STATUS

editing

proposed

#2 by Robert Price at Fri Jul 21 16:44:31 EDT 2017

NAME

allocated for Robert PriceNumbers k such that (316*10^k - 1)/9 is prime.

DATA

2, 3, 8, 9, 11, 14, 17, 23, 29, 38, 50, 129, 164, 578, 1592, 2951, 4505, 16826, 17438, 22748

OFFSET

1,1

COMMENTS

Numbers such that the digits 35 followed by k occurrences of the digit 1 is prime (see Example section).

a(21) > 10^5.

LINKS

Makoto Kamada, <a href="http://stdkmd.com/nrr">Factorization of near-repdigit-related numbers</a>.

Makoto Kamada, <a href="http://stdkmd.com/nrr/prime/primedifficulty.txt">Search for 351w.</a>

EXAMPLE

3 is in this sequence because (316*10^3 - 1)/9 = 35111 is prime.

Initial terms and primes associated:

a(1) = 2, 3511;

a(2) = 3, 35111;

a(3) = 8, 3511111111;

a(4) = 9, 35111111111;

a(5) = 11, 3511111111111; etc.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[(316*10^# - 1)/9] &]

CROSSREFS

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

KEYWORD

allocated

nonn,more,hard,new

AUTHOR

Robert Price, Jul 21 2017

STATUS

approved

editing