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.
%I A284285 #23 Jul 12 2024 21:59:08 %S A284285 5,9,25,45,61,189,289,489,7065,42229 %N A284285 Numbers k such that (2^k + 3)/5 is prime. %C A284285 For primes p = (2^a(n) + 3)/5, n >= 2, there are exactly 5 positive integers m for which the exponents of 2 and p in the prime power factorization of m! are both powers of 2 (for a proof see the Shevelev link (Theorem 2)). %C A284285 The sequence of such primes p begins 7, 103, 6710887, 7036874417767, etc. %C A284285 a(11) > 160000. - _Michael S. Branicky_, Jul 12 2024 %H A284285 V. Shevelev, <a href="http://journals.impan.gov.pl/aa/Inf/126-3-1.html">Compact integers and factorials</a>, Acta Arithmetica 126 (2007), no. 3, 195-236. %F A284285 a(n) == 1 (mod 4). %t A284285 Select[Range[7500], PrimeQ[(2^# + 3)/5] &] (* _Michael De Vlieger_, Mar 24 2017 *) %o A284285 (PARI) is(n)=n%4==1 && isprime((2^n+3)/5) \\ _Charles R Greathouse IV_, Mar 25 2017 %Y A284285 Cf. A000040, A283657. %K A284285 nonn,more %O A284285 1,1 %A A284285 _Vladimir Shevelev_, Mar 24 2017 %E A284285 Terms a(4)-a(9) from _Peter J. C. Moses_, Mar 24 2017 %E A284285 a(10) from _Giovanni Resta_, Mar 24 2017