cp's OEIS Frontend

A376265 Position of first appearance of n in A376264 (run-sums of first differences of nonsquarefree numbers), or 0 if there are none.

%I A376265 #6 Sep 27 2024 08:32:57
%S A376265 2,8,3,1,6222,14,308540,18
%N A376265 Position of first appearance of n in A376264 (run-sums of first differences of nonsquarefree numbers), or 0 if there are none.
%F A376265 A376264(a(n)) = n.
%e A376265 The sequence of nonsquarefree numbers (A013929) is:
%e A376265   4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ...
%e A376265 with first differences (A078147):
%e A376265   4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ...
%e A376265 with runs:
%e A376265   (4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ...
%e A376265 with sums (A376264):
%e A376265   4, 1, 3, 4, 4, 4, 1, 2, 1, 16, 1, 3, 2, 6, 4, 3, 1, 8, 3, 1, 4, 1, 3, 4, 4, ...
%e A376265 with first appearances at (A376265):
%e A376265   2, 8, 3, 1, 6222, 14, 308540, 18, ...
%t A376265 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A376265 q=Total/@Split[Differences[Select[Range[10000],!SquareFreeQ[#]&]]]//Most;
%t A376265 Table[Position[q,k][[1,1]],{k,mnrm[q]}]
%Y A376265 This is the position of first appearance of n in A376264.
%Y A376265 The sorted version is A376266.
%Y A376265 For run-lengths instead of firsts of run-sums we have A376267.
%Y A376265 For compression instead of firsts of run-sums we have A376312.
%Y A376265 A000040 lists the prime numbers, differences A001223.
%Y A376265 A000961 and A246655 list prime-powers, differences A057820.
%Y A376265 A003242 counts compressed compositions, ranks A333489.
%Y A376265 A005117 lists squarefree numbers, differences A076259 (ones A375927).
%Y A376265 A013929 lists nonsquarefree numbers, differences A078147.
%Y A376265 A333254 lists run-lengths of differences between consecutive primes.
%Y A376265 A376305 gives run-compression of first differences of squarefree numbers.
%Y A376265 A376307 gives run-sums of first differences of squarefree numbers.
%Y A376265 Cf. A037201, A053797, A053806, A120992, A373198, A373413, A373822, A375707, A376306, A376310, A376311.
%K A376265 nonn,more
%O A376265 1,1
%A A376265 _Gus Wiseman_, Sep 27 2024