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A056704 Numbers k such that 3*10^k + 1*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k. 1

%I #25 Jan 17 2019 13:44:05

%S 0,1,2,5,10,11,13,34,47,52,77,88,554,580,1310,1505,8537,15892,24022,

%T 27041,37922,40033,134122,165358,183760

%N Numbers k such that 3*10^k + 1*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (28*10^k - 1)/9 is prime.

%C Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 3*10^0 + 0 = 3*1 + 0 = 3 is prime. - _Robert Price_, Oct 28 2014

%C a(26) > 2*10^5. - _Robert Price_, Dec 19 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/31111.htm#prime">Prime numbers of the form 311...11</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>

%t Do[ If[ PrimeQ[ 3*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A068813.

%K hard,nonn

%O 1,3

%A _Robert G. Wilson v_, Aug 10 2000

%E Added zero by _Robert Price_, Oct 28 2014

%E a(18)-a(25) from Kamada data by _Robert Price_, Dec 19 2014

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)