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 A246783 #14 Nov 22 2014 13:47:12
%S A246783 1,1,1,1,67,67,67,67,67,54412,161342,161342,1214143,9915018,9915018,
%T A246783 68964006,68964006,810832784,19867608968,52415066804,119937255921,
%U A246783 272007811177
%N A246783 Smallest number m such that all the n numbers np(m+k-1), 0 < k < n+1 are equal, where np(t) is number of primes p with prime(t) < p < prime(t)^(1+1/t).
%C A246783 np(n) = A182134(n).
%C A246783 Conjecture: For every n, a(n) exists.
%C A246783 The np values for distinct terms of the sequence are: 1, 5, 11, 11, 16, 14, ... . It is interesting that for n = 1, 5, 11 & 14, np(a(n)) = n. What is the next term of this sequence (1, 5, 11, 14, ?, ... .)?
%C A246783 The sequence giving the np values of this sequence is A245101.
%C A246783 The sequence {1, 5, 11, 11, 16, 14} commented on above is expanded in A245098.
%C A246783 a(23) > 10^12. - _Robert Price_, Nov 12 2014
%C A246783 The next term of the sequence (1, 5, 11, 14, ?, ... .) commented on above is >22 and corresponds to t>10^12. - _Robert Price_, Nov 12 2014
%e A246783 a(9) = 67, since all the nine numbers np(67), np(67+1), np(67+2), ..., np(67+8) are equal and 67 is the smallest such number. Note that np(67) = 5.
%t A246783 np[n_]:=Length[Select[Range[Prime[n]+1,Prime[n]^(1+1/n)], PrimeQ]];a[n_]:=(For[m=1,Length[Union[Table[np[m+k-1],{k,n}]]]!=1,m++];m);Do[Print[a[n]],{n,15}]
%Y A246783 Cf. A000040, A182134.
%K A246783 nonn,more
%O A246783 1,5
%A A246783 _Farideh Firoozbakht_, Oct 13 2014
%E A246783 a(16)-a(22) from _Robert Price_, Nov 12 2014