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A056657 Numbers k such that 60*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k. 8

%I #28 Jul 04 2021 22:08:02

%S 0,1,5,7,8,10,19,22,40,62,65,118,121,148,251,283,304,591,745,874,1203,

%T 1363,2239,2402,5105,5775,5812,12455,14234,39605,55543,84238

%N Numbers k such that 60*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (20*10^k+1)/3 is prime.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/6/66667.htm#prime">Prime numbers of the form 66...667</a>.

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

%F a(n) = A096507(n) - 1.

%e 7, 67, 666667, 66666667, 666666667, 66666666667, etc. are primes.

%t Do[ If[ PrimeQ[ 60*(10^n - 1)/9 + 7 ], Print[n]], {n, 25556}]

%Y Cf. A002275, A093170, A096507.

%K nonn

%O 1,3

%A _Robert G. Wilson v_, Aug 09 2000

%E More terms from _Robert G. Wilson v_, Oct 22 2003

%E 2239,2402,5105,5775 from _Farideh Firoozbakht_, Dec 23 2003

%E 39605 and 55543 from Serge Batalov, Jun 2009

%E 84238 from Serge Batalov, Jul 06 2009 confirmed as next term by _Ray Chandler_, Feb 23 2012

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)