The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A370161 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A370161

a(n) is the dimension of the multilinear part of the free flexible algebra with n generators.
(history; published version)

#10 by N. J. A. Sloane at Sun Feb 18 12:20:35 EST 2024

STATUS

proposed

approved

#9 by Jon E. Schoenfield at Fri Feb 16 22:07:00 EST 2024

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Fri Feb 16 22:06:27 EST 2024

MATHEMATICA

Numerator[Rest[Map[#[[2]] &, a]]] (* A370161 this sequence *)

STATUS

proposed

editing

Discussion

Fri Feb 16

22:07

Jon E. Schoenfield: (problem corrected)

#7 by Clark Kimberling at Fri Feb 16 21:27:46 EST 2024

STATUS

editing

proposed

Discussion

Fri Feb 16

22:06

Jon E. Schoenfield: This is sequence A370161, so nothing in any of the fields of this sequence entry should refer to “A370161”.

#6 by Clark Kimberling at Fri Feb 16 21:27:08 EST 2024

MATHEMATICA

(* Peter J. C. Moses, Feb 6 06 2024 *)

#5 by Jon E. Schoenfield at Fri Feb 16 21:26:15 EST 2024

STATUS

proposed

editing

#4 by Clark Kimberling at Fri Feb 16 21:04:51 EST 2024

STATUS

editing

proposed

Discussion

Fri Feb 16

21:26

Jon E. Schoenfield: In the Mathematica section, please remove the self-reference and correct the format of the date.

#3 by Clark Kimberling at Fri Feb 16 20:56:41 EST 2024

NAME

allocated Numerator of fraction a(n)/b(n) < 3, where a(n) and b(n) are primes, and if p is a prime <= b(n) such that k/p < 3 for Clark Kimberlingsome prime k, then k = a(n) and p = b(n).

DATA

5, 13, 19, 31, 37, 67, 109, 127, 139, 157, 181, 199, 211, 307, 337, 379, 409, 487, 499, 541, 571, 577, 631, 751, 769, 787, 811, 829, 877, 919, 937, 991, 1009, 1039, 1117, 1201, 1291, 1297, 1327, 1381, 1399, 1459, 1471, 1567, 1621, 1669, 1759, 1777, 1801

OFFSET

1,1

COMMENTS

(a(n)/(b(n)) is a strictly increasing sequence that converges to 3.

EXAMPLE

5/2 < 13/5 < 19/7 < 31/11 < 37/13 < 67/23 < 109/37 < 127/43 < 139/47 < ...

MATHEMATICA

a = {{4, 4}}; r = 3; Do[If[# < Last[a][[2]], AppendTo[a, {n, #}]] &[

NextPrime[Prime[PrimePi[Prime[n]*r]]]/Prime[n]], {n, 1300}];

Numerator[Rest[Map[#[[2]] &, a]]] (* A370161 *)

Denominator[Rest[Map[#[[2]] &, a]]] (* A370162 *)

(* Peter J. C. Moses, Feb 6 2024 *)

CROSSREFS

Cf. A000040, A370162.

KEYWORD

allocated

nonn,frac

AUTHOR

Clark Kimberling, Feb 16 2024

STATUS

approved

editing

#2 by Clark Kimberling at Sat Feb 10 19:19:06 EST 2024

KEYWORD

allocating

allocated

#1 by Clark Kimberling at Sat Feb 10 19:19:06 EST 2024

NAME

allocated for Clark Kimberling

KEYWORD

allocating

STATUS

approved