A051426 -id:A051426 - cp's OEIS frontend

A159293 a(n) = smallest prime congruent to 1 mod A051426(n).

3, 5, 13, 73, 241, 241, 2521, 3361, 15121, 15121, 55441, 55441, 4324321, 4324321, 4324321, 4324321, 196035841, 196035841, 1862340481, 1862340481, 1862340481, 1862340481, 10708457761, 10708457761, 214169155201, 214169155201

Offset: 1

Zak Seidov, Apr 09 2009

nonn

A051426 Least common multiple of {2, 4, 6..., 2n}.

L1=2;A1={3};Do[L1=LCM[L1,n];k=1;While[ !PrimeQ[p=k*L1+1],k++ ];Print[p];AppendTo[A1,n],{n,4,60,2}]

A025547 Least common multiple of {1,3,5,...,2n-1}.

Original entry on oeis.org

1, 3, 15, 105, 315, 3465, 45045, 45045, 765765, 14549535, 14549535, 334639305, 1673196525, 5019589575, 145568097675, 4512611027925, 4512611027925, 4512611027925, 166966608033225, 166966608033225, 6845630929362225, 294362129962575675, 294362129962575675

Offset: 1

Clark Kimberling

This sequence coincides with the sequence f(n) = denominator of 1 + 1/3 + 1/5 + 1/7 + ... + 1/(2n-1) iff n <= 38. But a(39) = 6414924694381721303722858446525, f(39) = 583174972216520118520259858775. - T. D. Noe, Aug 04 2004 [See A350670(n-1).]
Coincides for n=1..42 with the denominators of a series for Pi*sqrt(2)/4 and then starts to differ. See A127676.
a(floor((n+1)/2)) = gcd(a(n), A051426(n)). - Reinhard Zumkeller, Apr 25 2011
A051417(n) = a(n+1)/a(n).

T. D. Noe, Table of n, a(n) for n = 1..200
Yue-Wu Li and Feng Qi, A New Closed-Form Formula of the Gauss Hypergeometric Function at Specific Arguments, Axioms (2024) Vol. 13, Art. No. 317. See p. 11 of 24.
Eric Weisstein's World of Mathematics, Jeep Problem, Pi, Pi Continued Fraction, Least Common Multiple
Wikipedia, Least common multiple
Index entries for sequences related to lcm's

Cf. A007509, A025550, A075135. The numerators are in A074599.
Cf. A003418 (LCM of {1..n}).
Cf. A005408, A350670.

a025547 n = a025547_list !! (n-1)
a025547_list = scanl1 lcm a005408_list
-- Reinhard Zumkeller, Oct 25 2013, Apr 25 2011

A025547:=proc(n) local i,t1; t1:=1; for i from 1 to n do t1:=lcm(t1,2*i-1); od: t1; end;
f := n->denom(add(1/(2*k-1),k=0..n)); # a different sequence!

a = 1; Join[{1}, Table[a = LCM[a, n], {n, 3, 125, 2}]] (* Zak Seidov, Jan 18 2011 *)
nn=30;With[{c=Range[1,2*nn,2]},Table[LCM@@Take[c,n],{n,nn}]] (* Harvey P. Dale, Jan 27 2013 *)

a(n)=lcm(vector(n,k,2*k-1)) \\ Charles R Greathouse IV, Nov 20 2012

# generates initial segment of sequence
from math import gcd
from itertools import accumulate
def lcm(a, b): return a * b // gcd(a, b)
def aupton(nn): return list(accumulate((2*i+1 for i in range(nn)), lcm))
print(aupton(23)) # Michael S. Branicky, Mar 28 2022

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A051905 Duplicate of A051426.

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A159293 a(n) = smallest prime congruent to 1 mod A051426(n).

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A025547 Least common multiple of {1,3,5,...,2n-1}.

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