A378370 - OEIS

%I #11 Nov 30 2024 23:44:52

%S 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 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 2,1,0,1,0,5,4,3,2,1,0,1,0,1,0,5,4,3,2

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

%C Prime powers allowing 1 are listed by A000961.

%F a(n) = A000015(n) - n.

%F a(n) = A377282(n - 1) - 1 for n > 1.

%t Table[NestWhile[#+1&,n,#>1&&!PrimePowerQ[#]&]-n,{n,100}]

%Y Sequences obtained by adding n to each term are placed in parentheses below.

%Y For prime instead of prime power we have A007920 (A007918), strict A013632.

%Y For perfect power we have A074984 (A377468), opposite A069584 (A081676).

%Y For squarefree we have A081221 (A067535).

%Y The restriction to the prime numbers is A377281 (A345531).

%Y The strict version is A377282 = a(n) + 1.

%Y For non prime power instead of prime power we have A378371 (A378372).

%Y The opposite version is A378457, strict A276781.

%Y A000015 gives the least prime power >= n, opposite A031218.

%Y A000040 lists the primes, differences A001223.

%Y A000961 and A246655 list the prime powers, differences A057820.

%Y A024619 and A361102 list the non prime powers, differences A375708 and A375735.

%Y A151800 gives the least prime > n.

%Y Prime-powers between primes: A053607, A080101, A304521, A366833, A377057.

%Y Cf. A001597, A053707, A065514, A065890, A343249, A376596, A376597, A377051, A377054, A377289, A377781.

%K nonn

%O 1,14

%A _Gus Wiseman_, Nov 27 2024