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%I #34 Jan 20 2023 15:37:06
%S 1,2,4,5,8,23,29,40,131,136,215,611,767,2153,2576,22973,42689,85712,
%T 85864,112067,538508,631715
%N Numbers k such that (10^k - 1)/9 + 6 is prime.
%C Values indicate primes of the form "(k-1) ones followed by a seven". Related to the base-10 repunit primes.
%C Some of the larger entries may only correspond to probable primes.
%C a(20) > 10^5. - _Robert Price_, Jan 11 2015
%C Corresponding primes are equal to (10^k + 53)/9. - _Robert Price_, Jan 11 2015
%C a(23) > 6.7*10^5, determined by Rytis Slatkevičius. - _Jeppe Stig Nielsen_, Jan 20 2023
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11117.htm#prime">Prime numbers of the form 11...117</a>.
%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%F a(n) = A056655(n) + 1 for all n >= 0.
%t Do[ If[ PrimeQ[(10^n - 1)/9 + 6], Print[n]], {n, 0, 5000}] (* _Robert G. Wilson v_, Oct 14 2004 *)
%o (PARI) for (i=1,1000,if(isprime((10^i-1)/9 + 6),print1(i,","))) \\ Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Aug 23 2004
%Y Cf. A004023, A056655, A097683, A097685.
%K nonn
%O 1,2
%A _Carl R. White_, Aug 19 2004
%E a(12)-a(13) from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Aug 23 2004
%E a(12)-a(15) from _Rick L. Shepherd_, Aug 23 2004
%E a(16)-a(19) from _Robert Price_, Jan 11 2015
%E a(20) from _Serge Batalov_ and a(21)-a(22) from Rytis Slatkevičius communicated by _Jeppe Stig Nielsen_, Jan 20 2023
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