cp's OEIS Frontend

A378370 Distance between n and the least prime power >= n, allowing 1.

%I A378370 #11 Nov 30 2024 23:44:52
%S A378370 0,0,0,0,0,1,0,0,0,1,0,1,0,2,1,0,0,1,0,3,2,1,0,1,0,1,0,1,0,1,0,0,4,3,
%T A378370 2,1,0,3,2,1,0,1,0,3,2,1,0,1,0,3,2,1,0,5,4,3,2,1,0,1,0,2,1,0,2,1,0,3,
%U A378370 2,1,0,1,0,5,4,3,2,1,0,1,0,1,0,5,4,3,2
%N A378370 Distance between n and the least prime power >= n, allowing 1.
%C A378370 Prime powers allowing 1 are listed by A000961.
%F A378370 a(n) = A000015(n) - n.
%F A378370 a(n) = A377282(n - 1) - 1 for n > 1.
%t A378370 Table[NestWhile[#+1&,n,#>1&&!PrimePowerQ[#]&]-n,{n,100}]
%Y A378370 Sequences obtained by adding n to each term are placed in parentheses below.
%Y A378370 For prime instead of prime power we have A007920 (A007918), strict A013632.
%Y A378370 For perfect power we have A074984 (A377468), opposite A069584 (A081676).
%Y A378370 For squarefree we have A081221 (A067535).
%Y A378370 The restriction to the prime numbers is A377281 (A345531).
%Y A378370 The strict version is A377282 = a(n) + 1.
%Y A378370 For non prime power instead of prime power we have A378371 (A378372).
%Y A378370 The opposite version is A378457, strict A276781.
%Y A378370 A000015 gives the least prime power >= n, opposite A031218.
%Y A378370 A000040 lists the primes, differences A001223.
%Y A378370 A000961 and A246655 list the prime powers, differences A057820.
%Y A378370 A024619 and A361102 list the non prime powers, differences A375708 and A375735.
%Y A378370 A151800 gives the least prime > n.
%Y A378370 Prime-powers between primes: A053607, A080101, A304521, A366833, A377057.
%Y A378370 Cf. A001597, A053707, A065514, A065890, A343249, A376596, A376597, A377051, A377054, A377289, A377781.
%K A378370 nonn
%O A378370 1,14
%A A378370 _Gus Wiseman_, Nov 27 2024