cp's OEIS Frontend

A110969 Length of the runs of ones in A014963.

%I A110969 #15 Jun 18 2024 20:37:01
%S A110969 1,1,1,1,2,1,3,1,1,1,1,4,3,1,3,1,3,5,1,2,2,3,1,5,1,1,5,7,3,1,3,1,3,7,
%T A110969 3,1,2,5,1,9,1,5,5,3,1,3,5,1,9,1,3,1,11,11,3,1,3,5,1,1,7,4,5,5,1,5,3,
%U A110969 1,5,3,13,3,1,3,13,5,5,3,1,3,5,1,5,5,5,3,5,7,3,7
%N A110969 Length of the runs of ones in A014963.
%C A110969 Unbounded sequence.
%C A110969 From A373669 we see that 10 first appears at a(28195574) = 10.
%C A110969 Also run-lengths of non-prime-powers (assuming 1 is not a prime-power), where a run of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by one. Also nonzero differences of consecutive prime-powers minus one. - _Gus Wiseman_, Jun 18 2024
%H A110969 Andrew Howroyd, <a href="/A110969/b110969.txt">Table of n, a(n) for n = 1..10000</a>
%e A110969 a(5)=2 because the fifth run of ones in A014963 is of length 2.
%t A110969 Length /@ SplitBy[Table[Exp[MangoldtLambda[n]], {n, 400}], # != 1 &][[ ;; -1 ;; 2]] (* _Michael De Vlieger_, Mar 21 2024 *)
%t A110969 DeleteCases[Differences[Select[Range[100],PrimePowerQ]]-1,0] (* _Gus Wiseman_, Jun 18 2024 *)
%o A110969 (PARI) \\ b(n) returns boolean of A014963(n) == 1.
%o A110969 b(n)={my(t); !isprime(if(ispower(n, ,&t), t, n))}
%o A110969 seq(n)={my(k=1, i=0, L=List()); while(#L<n, i++; if(!b(i), if(i>k, listput(L, i-k)); k = i+1)); Vec(L)} \\ _Andrew Howroyd_, Jan 02 2020
%Y A110969 Cf. A014963.
%Y A110969 Positions of first appearances are A373670, sorted A373669.
%Y A110969 For runs of prime-powers:
%Y A110969 - length A174965, antiruns A373671
%Y A110969 - min A373673, antiruns A120430
%Y A110969 - max A373674, antiruns A006549
%Y A110969 - sum A373675, antiruns A373576
%Y A110969 For runs of non-prime-powers:
%Y A110969 - length A110969 (this sequence), antiruns A373672
%Y A110969 - min A373676, antiruns A373575
%Y A110969 - max A373677, antiruns A255346
%Y A110969 - sum A373678, antiruns A373679
%Y A110969 A000961 lists all powers of primes. A246655 lists just prime-powers.
%Y A110969 A057820 gives first differences of consecutive prime-powers, gaps A093555.
%Y A110969 A356068 counts non-prime-powers up to n.
%Y A110969 A361102 lists all non-prime-powers (A024619 if not including 1).
%Y A110969 Various run-lengths: A053797, A120992, A175632, A176246.
%Y A110969 Various antirun-lengths: A027833, A373127, A373403, A373409.
%Y A110969 Cf. A001359, A008864, A067774, A251092.
%K A110969 nonn
%O A110969 1,5
%A A110969 _Franz Vrabec_, Sep 27 2005
%E A110969 Terms a(41) and beyond from _Andrew Howroyd_, Jan 02 2020