cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A103054 Numbers k such that 7*10^k + 2*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

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%I A103054 #30 Jul 12 2025 16:04:01
%S A103054 1,3,4,7,9,13,33,37,76,147,297,1851,3457,3609,45219
%N A103054 Numbers k such that 7*10^k + 2*R_k + 7 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A103054 Also numbers k such that (65*10^k+61)/9 is prime.
%C A103054 a(16) > 10^5. - _Robert Price_, Oct 01 2015
%H A103054 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/72229.htm#prime">Prime numbers of the form 722...229</a>.
%H A103054 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A103054 a(n) = A101136(n) + 1.
%t A103054 Do[ If[ PrimeQ[(65*10^n + 61)/9], Print[n]], {n, 0, 10000}]
%t A103054 Select[Range[10000], PrimeQ[(65 10^# + 61)/9] &] (* _Vincenzo Librandi_, Oct 02 2015 *)
%o A103054 (Magma) [n: n in [0..3*10^2]| IsPrime((65*10^n+61) div 9)]; // _Vincenzo Librandi_, Oct 02 2015
%o A103054 (PARI) for(n=1, 1e4, if (isprime((65*10^n+61)/9), print1(n", "))) \\ _Altug Alkan_, Oct 02 2015
%Y A103054 Cf. A002275, A101136.
%K A103054 more,nonn
%O A103054 1,2
%A A103054 _Robert G. Wilson v_, Jan 19 2005
%E A103054 a(15) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013