cp's OEIS Frontend

A366833 Number of times n appears in A362965 (number of primes <= the n-th prime power).

%I A366833 #36 Jan 13 2025 13:15:03
%S A366833 1,2,1,3,1,2,1,1,3,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,1,1,1,1,1,3,2,1,1,1,
%T A366833 1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,
%U A366833 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A366833 Number of times n appears in A362965 (number of primes <= the n-th prime power).
%C A366833 Conjecture: a(n) can be only 1, 2, or 3 (with the first occurrences of 3 appearing at n = 4, 9, 30, 327 and 3512).
%C A366833 One less than the number of prime powers between prime(n) and prime(n+1), inclusive. - _Gus Wiseman_, Jan 09 2025
%H A366833 Paolo Xausa, <a href="/A366833/b366833.txt">Table of n, a(n) for n = 1..10000</a>
%H A366833 Paolo Xausa, <a href="/A366833/a366833.png">1200 X 1200 raster image of a(n)</a>, n = 1..1440000, read left to right, top to bottom, showing a(n) = 1 in blue, a(n) = 2 in white and a(n) = 3 in red.
%F A366833 a(n) = A080101(n) + 1. - _Gus Wiseman_, Jan 09 2025
%t A366833 With[{upto=1000},Map[Length,Most[Split[PrimePi[Select[Range[upto],PrimePowerQ]]]]]] (* Considers prime powers up to 1000 *)
%Y A366833 Run lengths of A362965.
%Y A366833 Subtracting one gives A080101.
%Y A366833 For non prime powers we have A368748.
%Y A366833 Positions of terms > 1 are A377057.
%Y A366833 Positions of 1 are A377286.
%Y A366833 Positions of 2 are A377287.
%Y A366833 For perfect powers we have A377432.
%Y A366833 For squarefree we have A373198.
%Y A366833 A000015 gives the least prime power >= n, difference A377282.
%Y A366833 A000040 lists the primes, differences A001223.
%Y A366833 A000961 lists the powers of primes, differences A057820.
%Y A366833 A024619 and A361102 list the non prime powers, differences A375708 and A375735.
%Y A366833 A031218 gives the greatest prime power <= n, difference A276781.
%Y A366833 A046933(n) counts the interval from A008864(n) to A006093(n+1).
%Y A366833 A246655 lists the prime powers not including 1.
%Y A366833 A366835 counts primes between prime powers.
%Y A366833 Cf. A053607, A053706, A065514, A068435, A080102, A304521, A345531, A377289.
%Y A366833 Cf. A024620, A027883, A067871, A075526, A080769, A151800, A377436, A379157.
%K A366833 nonn
%O A366833 1,2
%A A366833 _Paolo Xausa_, Oct 25 2023