cp's OEIS Frontend

A377055 Position of first appearance of zero in the n-th differences of the prime-powers (A246655), or 0 if it does not appear.

%I A377055 #24 Nov 04 2024 09:30:27
%S A377055 0,0,1,1,4,48,61,83,29,57,290,121,7115,14207,68320,14652,149979,
%T A377055 122704,481540,980376,632441,29973,25343678,50577935,7512418,
%U A377055 210836403,67253056,224083553,910629561,931524323,452509699,2880227533,396690327,57954538325,77572935454,35395016473
%N A377055 Position of first appearance of zero in the n-th differences of the prime-powers (A246655), or 0 if it does not appear.
%H A377055 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A377055.py">Python program</a>.
%e A377055 The fourth differences of A246655 begin: 1, -3, 3, 0, -2, 2, ... so a(4) = 4.
%t A377055 nn=10000;
%t A377055 u=Table[Differences[Select[Range[nn],PrimePowerQ],k],{k,2,16}];
%t A377055 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A377055 m=Table[Position[u[[k]],0][[1,1]], {k,mnrm[Union[First/@Position[u,0]]]}]
%Y A377055 The version for primes is A376678, noncomposites A376855, composites A377037.
%Y A377055 For squarefree numbers we have A377042, nonsquarefree A377050.
%Y A377055 These are the positions of first zeros in each row of A377051.
%Y A377055 For antidiagonal-sums we have A377052, absolute A377053.
%Y A377055 For leaders we have A377054, for primes A007442 or A030016.
%Y A377055 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377055 A000961 lists the powers of primes, differences A057820.
%Y A377055 A008578 lists the noncomposites, differences A075526.
%Y A377055 A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.
%Y A377055 A246655 lists the prime-powers, differences A057820 (except first term).
%Y A377055 Cf. A025475, A053707, A093555, A174965, A175804, A361102, A376340, A376596, A377056.
%K A377055 nonn
%O A377055 0,5
%A A377055 _Gus Wiseman_, Oct 22 2024
%E A377055 a(12)-a(27) from _Pontus von Brömssen_, Oct 22 2024
%E A377055 a(28)-a(30) from _Chai Wah Wu_, Oct 23 2024
%E A377055 a(31)-a(35) from _Lucas A. Brown_, Nov 03 2024