Question

Is there a polynomial (or series) expression for summing $S_d(a,N)=\sum_{k=0}^{N-1} \log(1+{1\over a+k \cdot d})$? (perhaps Bernoulli-type)

score 222 · Answer 1 · 2026-04-09 04:50:57

222

Views

Is there a polynomial (or series) expression for summing $S_d(a,N)=\sum_{k=0}^{N-1} \log(1+{1\over a+k \cdot d})$? (perhaps Bernoulli-type)

Published on 09 Apr 2026 - 4:50

score 172 · Answer 2 · 2026-04-13 07:55:21

172

Views

Polynomial divided by a monomial in some extended Collatz Shortcut function

Published on 13 Apr 2026 - 7:55

score 388 · Answer 3 · 2026-05-10 19:22:04

388

Views

Collatz $2x + 1$ conjecture?

Published on 10 May 2026 - 19:22

score 4.5k · Answer 4 · 2026-05-10 14:55:54

4.5k

Views

Why is the Collatz Conjecture so difficult to prove or disprove?

Published on 10 May 2026 - 14:55

score 216 · Answer 5 · 2026-05-10 13:50:05

216

Views

"What is the specific mathematical reason behind the origin of the Collatz Conjecture that makes it difficult to solve it?

Published on 10 May 2026 - 13:50

score 414 · Answer 6 · 2026-04-14 07:30:44

414

Views

How to prove property of Collatz Conjecture trees (3x+1 Problem)

Published on 14 Apr 2026 - 7:30

score 506 · Answer 7 · 2026-03-25 12:15:15

506

Views

Preserving historical information of the Collatz function?

Published on 25 Mar 2026 - 12:15

score 177 · Answer 8 · 2026-04-17 11:38:22

177

Views

$3n+1$ graph and shared vertices

Published on 17 Apr 2026 - 11:38

score 227 · Answer 9 · 2026-04-09 07:31:21

227

Views

Number of Collatz steps for Mersenne numbers

Published on 09 Apr 2026 - 7:31

score 96 · Answer 10 · 2026-04-14 13:06:35

96

Views

Cycles in bit-limited verson of Collatz map

Published on 14 Apr 2026 - 13:06

score 1.2k · Answer 11 · 2026-04-14 17:50:34

1.2k

Views

A possible way to prove non-cyclicity of eventual counterexamples of the Collatz conjecture?

Published on 14 Apr 2026 - 17:50

score 511 · Answer 12 · 2026-04-13 04:20:48

511

Views

What formula could generate this sequence related to the Collatz conjecture

Published on 13 Apr 2026 - 4:20

score 340 · Answer 13 · 2026-04-16 08:50:04

340

Views

What is the sequence of accumulation points in the 2-adic space, of the Collatz graph?

Published on 16 Apr 2026 - 8:50

score 400 · Answer 14 · 2026-04-14 10:25:58

400

Views

New record for for lower bound of non-trivial cycle lengths of Collatz sequences?

Published on 14 Apr 2026 - 10:25

score 117 · Answer 15 · 2026-04-14 03:18:40

117

Views

Why does plotting $\frac{3n+1}{2^k}$ give several apparently straight lines?

Published on 14 Apr 2026 - 3:18

List Question

Is there a polynomial (or series) expression for summing $S_d(a,N)=\sum_{k=0}^{N-1} \log(1+{1\over a+k \cdot d})$? (perhaps Bernoulli-type)

Polynomial divided by a monomial in some extended Collatz Shortcut function

Collatz $2x + 1$ conjecture?

Why is the Collatz Conjecture so difficult to prove or disprove?

"What is the specific mathematical reason behind the origin of the Collatz Conjecture that makes it difficult to solve it?

How to prove property of Collatz Conjecture trees (3x+1 Problem)

Preserving historical information of the Collatz function?

$3n+1$ graph and shared vertices

Number of Collatz steps for Mersenne numbers

Cycles in bit-limited verson of Collatz map

A possible way to prove non-cyclicity of eventual counterexamples of the Collatz conjecture?

What formula could generate this sequence related to the Collatz conjecture

What is the sequence of accumulation points in the 2-adic space, of the Collatz graph?

New record for for lower bound of non-trivial cycle lengths of Collatz sequences?

Why does plotting $\frac{3n+1}{2^k}$ give several apparently straight lines?

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