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 A177459 #14 Jan 23 2025 10:23:27 %S A177459 19,131,34,19,35,35,35,67,259,575,67,67,67,131,259,515,1027,131,131, %T A177459 131,131,131,259,259,259,514,515,515,515,8195 %N A177459 The maximal positive integer m for which the exponents of 2 and prime(n) in the prime power factorization of m! are both powers of 2. %C A177459 Or a(n) is the maximal m for which the Fermi-Dirac representation of m! (see comment in A050376) contains single power of 2 and single power of prime(n). %H A177459 Vladimir Shevelev, <a href="https://eudml.org/doc/277854">Compact integers and factorials</a>, Acta Arithmetica 126 (2007), no. 3, 195-236. %F A177459 a(2)=19, a(3)=131; if prime(n) has the form (2^(4k+1)+3)/5 for k>=1,then a(n)=5*prime(n)-1; if prime(n)>=17 is Fermat prime, then a(n)=2*prime(n)+1; if prime(n) has the form 2^k+3 for k>=3, then a(n)=2*prime(n)-3; otherwise, if prime(n) is in interval [2^(k-1)+5, 2^k) for k>=4, then a(n)=3+2^(k+floor(log_2((p_n-5)/(2^k-prime(n)))). In any case, a(n)<=(1/2)*(prime(n)+1)^2+3. Equality holds for Mersenne primes>=31. %e A177459 For n=31, prime(n)=127 is Mersenne primes. Thus a(31)=(1/2)*128^2+3=8195. %Y A177459 Cf. A000142, A177436, A177378, A177355, A177349, A177458, A177498, A050376, A169655, A169661. %K A177459 nonn,more %O A177459 2,1 %A A177459 _Vladimir Shevelev_, May 09 2010