A376573 -id:A376573 - cp's OEIS frontend

A376745 Numbers that are not pentagonal pyramidal numbers.

2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Chai Wah Wu, Oct 03 2024

Complement of A002411. Numbers not of the form k^2*(k+1)/2.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Cf. A002411, A000330, A000537, A302058, A376573.

p=71;l=Floor[(2p)^(1/3)];Complement[Range[p],Table[n^2 (n + 1)/2, {n, 0, l}]] (* James C. McMahon, Oct 07 2024 *)

from sympy import integer_nthroot
def A376745(n): return n+(m:=integer_nthroot(k:=n<<1,3)[0])-(k<=m*(m-1)*(m+2))

a(n) = n+m if 2n>m(m-1)(m+2) and a(n) = n+m-1 otherwise where m = floor((2n)^(1/3)).

A377306 Numbers that are not the sum of the first k fourth powers.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset: 1

Chai Wah Wu, Oct 23 2024

Complement of A000538.

Cf. A133137, A000330, A000537, A302058, A376573, A000538, A376745.

lim=69;l4=Ceiling[lim^(1/4)];Complement[Range[lim],Accumulate[Range[0, l4]^4]] (* James C. McMahon, Oct 24 2024 *)

from sympy import integer_nthroot
def A377306(n): return n+(m:=integer_nthroot(5*n,5)[0])-(30*n<=m*(m-1)*(m*(m*(3*((m<<1)+7))+31)+31))

a(n) = n+m if 30n > m(m-1)(6m^3+21m^2+31m+31) and a(n) = n+m-1 otherwise, where m = floor((5n)^(1/5)).

cp's OEIS Frontend

A376745 Numbers that are not pentagonal pyramidal numbers.

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