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A377784 First-differences of A377783 (least nonsquarefree number > prime(n)).

%I A377784 #8 Nov 19 2024 17:32:04
%S A377784 0,4,0,4,4,2,2,4,8,0,8,4,0,4,6,6,3,5,4,3,5,4,6,8,6,0,4,4,4,12,4,8,0,
%T A377784 10,2,8,4,4,7,5,4,8,4,2,2,12,12,4,4,2,6,2,10,8,4,6,2,7,5,0,10,14,4,3,
%U A377784 5,12,6,10,2,6,4,8,7,5,4,8,8,4,8,8,3,9,4,4
%N A377784 First-differences of A377783 (least nonsquarefree number > prime(n)).
%C A377784 There are no consecutive 0's.
%C A377784 Does this sequence contain every positive integer > 1?
%t A377784 Differences[Table[NestWhile[#+1&,Prime[n],SquareFreeQ[#]&],{n,100}]]
%Y A377784 Positions of 0's are A068361.
%Y A377784 The opposite for squarefree is A378038, differences of A112925.
%Y A377784 For prime-power instead of nonsquarefree and primes + 1 we have A377703, first-differences of A345531.
%Y A377784 First-differences of A377783, union A378040.
%Y A377784 The opposite is A378034 (differences of A378032), restriction of A378036 (differences A378033).
%Y A377784 For squarefree instead of nonsquarefree we have A378037, first-differences of A112926.
%Y A377784 Restriction of A378039 (first-differences of A120327) to the primes.
%Y A377784 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377784 A005117 lists the squarefree numbers.
%Y A377784 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A377784 A061398, A068360, A337030, A377430, A377431 count squarefree numbers between primes.
%Y A377784 A061399, A068361, A378086 count nonsquarefree numbers between primes.
%Y A377784 A070321 gives the greatest squarefree number up to n.
%Y A377784 Cf. A000015, A013928, A053797, A053806, A072284, A224363.
%Y A377784 Cf. A377047, A377048, A377049.
%Y A377784 Cf. A378082, A378083, A378084.
%K A377784 nonn
%O A377784 1,2
%A A377784 _Gus Wiseman_, Nov 18 2024