cp's OEIS Frontend

A338900 Difference between the two prime indices of the n-th squarefree semiprime.

%I A338900 #7 Nov 20 2020 17:19:28
%S A338900 1,2,3,1,2,4,5,3,6,1,7,4,8,5,2,6,9,10,3,7,11,1,12,4,13,8,2,9,14,5,15,
%T A338900 10,6,16,3,17,11,12,4,18,13,19,1,7,20,8,21,14,5,22,15,23,16,9,2,24,17,
%U A338900 25,6,10,26,3,18,27,11,7,28,19,1,29,12,20,2,21,4
%N A338900 Difference between the two prime indices of the n-th squarefree semiprime.
%C A338900 A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
%C A338900 Is this sequence an anti-run, i.e., are there no adjacent equal parts? I have verified this conjecture up to n = 10^6. - _Gus Wiseman_, Nov 18 2020
%F A338900 If the n-th squarefree semiprime is prime(x) * prime(y) with x < y, then a(n) = y - x.
%F A338900 a(n) = A270652(n) - A270650(n).
%t A338900 -Subtract@@PrimePi/@First/@FactorInteger[#]&/@Select[Range[100],SquareFreeQ[#]&&PrimeOmega[#]==2&]
%Y A338900 A176506 is the not necessarily squarefree version.
%Y A338900 A338899 has row-differences equal to this sequence.
%Y A338900 A338901 gives positions of first appearances.
%Y A338900 A001221 counts distinct prime indices.
%Y A338900 A001222 counts prime indices.
%Y A338900 A001358 lists semiprimes.
%Y A338900 A002100 and A338903 count partitions using squarefree semiprimes.
%Y A338900 A004526 counts 2-part partitions, with strict case A140106 (shifted left).
%Y A338900 A005117 lists squarefree numbers.
%Y A338900 A006881 lists squarefree semiprimes, with odds A046388 and evens A100484.
%Y A338900 A065516 gives first differences of semiprimes.
%Y A338900 A166237 gives first differences of squarefree semiprimes.
%Y A338900 A270650 and A270652 give the prime indices of squarefree semiprimes.
%Y A338900 A338912 and A338913 give the prime indices of semiprimes.
%Y A338900 Cf. A000040, A056239, A112798, A167171, A320656, A320891, A320894, A320911, A338898, A338905, A338908.
%K A338900 nonn
%O A338900 1,2
%A A338900 _Gus Wiseman_, Nov 16 2020