The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A003420 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A003420

Values of m in the discriminant D = -4*m leading to a new maximum of the L-function of the Dirichlet series L(1) = Sum_{k=1..oo} Kronecker(D,k)/k.
(history; published version)

#35 by Michael De Vlieger at Sat Aug 27 21:31:23 EDT 2022

STATUS

proposed

approved

#34 by Joerg Arndt at Sat Aug 27 07:21:17 EDT 2022

STATUS

editing

proposed

#33 by Joerg Arndt at Sat Aug 27 07:20:28 EDT 2022

EXTENSIONS

3 further term terms < 10^6 added by Hugo Pfoertner, Aug 27 2022

STATUS

proposed

editing

#32 by Hugo Pfoertner at Sat Aug 27 06:31:27 EDT 2022

STATUS

editing

proposed

#31 by Hugo Pfoertner at Sat Aug 27 06:17:47 EDT 2022

DATA

1, 2, 5, 11, 14, 26, 41, 89, 101, 194, 314, 341, 689, 1091, 1154, 1889, 2141, 3449, 3506, 5561, 6254, 8126, 8774, 10709, 13166, 15461, 23201, 24569, 30014, 81149, 81626, 162686, 243374, 644474, 839354, 879941

EXTENSIONS

Term 6254 deleted and 3 further term < 10^6 added by Hugo Pfoertner, Aug 27 2022

STATUS

proposed

editing

Discussion

Sat Aug 27

06:31

Hugo Pfoertner: Further precision increase to \p40000 confirms presence of 6254. Please excuse the unjustified alarm!

#30 by Hugo Pfoertner at Sat Aug 27 06:07:43 EDT 2022

STATUS

editing

proposed

Discussion

Sat Aug 27

06:13

Hugo Pfoertner: Sorry, precision in PARI was \p10000. Otherwise 81149 is not found.

#29 by Hugo Pfoertner at Sat Aug 27 06:05:12 EDT 2022

DATA

EXTENSIONS

Term 6254 deleted and 3 further term < 10^6 added by Hugo Pfoertner, Aug 27 2022

STATUS

approved

editing

Discussion

Sat Aug 27

06:07

Hugo Pfoertner: Compared to the terms given by Buell, I get different results for 6254. With the PARI function sumalt and \p5000 I get with L_1:=L(0): L_1(5561)= 2.78214..., L_1(6254)=2.7811667. .. and L_1(8126)= 2.7865067868..., i.e., 6254 would not be a term. I cannot judge whether sumalt contains a suitably precise method. In any case, all other terms are confirmed and the values of L(0) agree approximately with the results from 1973 and 1977. I would be very grateful if someone could independently verify this. A summation with Mathematica's NSum[KroneckerSymbol[-4*6254, i]/i, {i, 1, Infinity}, AccuracyGoal -> 100, PrecisionGoal -> 100] returns an obviously wrong result with 2.264352838648168.

#28 by Michael De Vlieger at Fri Aug 26 18:50:14 EDT 2022

STATUS

proposed

approved

#27 by Hugo Pfoertner at Fri Aug 26 17:58:55 EDT 2022

STATUS

editing

proposed

#26 by Hugo Pfoertner at Fri Aug 26 17:58:19 EDT 2022

CROSSREFS

Cf. A331949, which has almost identical terms.

STATUS

approved

editing