The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A218164 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A218164

a(n) is the smallest positive integer k such that k^64 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 128*b (see A208177).
(history; published version)

#13 by Alois P. Heinz at Tue Jan 19 15:32:08 EST 2021

STATUS

editing

approved

#12 by Alois P. Heinz at Tue Jan 19 15:31:23 EST 2021

MATHEMATICA

aa = {}; Do[p = Prime[n]; If[Mod[p, 128] == 1, k = 1; While[ ! Mod[k^64 + 1, p] == 0, k++ ]; AppendTo[aa, k]], {n, 5000}]; aa

#11 by Alois P. Heinz at Tue Jan 19 15:30:41 EST 2021

COMMENTS

A208177(n) : primes of the form 128n128*k+1.

EXAMPLE

a(1) = 9 because 9^64+1 = 2 * 257 * 275201 * 138424618868737 * 3913786281514524929 * 153849834853910661121 with A208177(1) = 257.

* 257 * 275201 * 138424618868737 * 3913786281514524929 * 153849834

853910661121 with A208177(1) = 257.

#10 by Alois P. Heinz at Tue Jan 19 15:27:44 EST 2021

STATUS

proposed

editing

#9 by Harvey P. Dale at Tue Jan 19 15:00:27 EST 2021

STATUS

editing

proposed

Discussion

Tue Jan 19

15:27

Alois P. Heinz: changes are correct ...

#8 by Harvey P. Dale at Tue Jan 19 15:00:20 EST 2021

STATUS

proposed

editing

#7 by Harvey P. Dale at Tue Jan 19 15:00:12 EST 2021

STATUS

editing

proposed

#6 by Harvey P. Dale at Tue Jan 19 14:59:16 EST 2021

DATA

9, 21, 5, 38, 21, 31, 33, 63, 42, 66, 118, 131, 202, 29, 28, 31, 58, 171, 94, 182, 309, 182, 81, 272, 110, 175, 657, 491, 42, 100, 523, 244, 168, 199, 45, 145, 138, 79, 73, 357, 826, 210, 541, 523, 215, 98, 220, 1478, 22, 92, 178, 50, 709, 250, 2523, 630, 18, 218, 7, 12

MATHEMATICA

spi[n_]:=Module[{k=1}, While[PowerMod[k, 64, n]!=n-1, k++]; k]; spi/@Select[128 Range[500]+1, PrimeQ] (* Harvey P. Dale, Jan 19 2021 *)

EXTENSIONS

Corrected by Harvey P. Dale, Jan 19 2021

STATUS

approved

editing

Discussion

Tue Jan 19

15:00

Harvey P. Dale: Please check my Mma program and the terms it generates because it produced some terms that disagree with those previously shown for the sequence.

#5 by T. D. Noe at Mon Oct 22 18:27:54 EDT 2012

STATUS

editing

approved

#4 by T. D. Noe at Mon Oct 22 18:27:50 EDT 2012

NAME

a(n) is the smallest positive integer k such that k^64 + 1 == 0 mod p, where p is the n-th prime of the form 1 + 128*b (see A208177(n).

MATHEMATICA

aa = {}; Do[If[Mod[p = Prime[n], ; If[Mod[p, 128] == 1, k = 1; While[ ! Mod[k^64 + 1, Prime[n]p] == 0, k++ ]; AppendTo[aa, k]], {n, 1, 5000}]; aa

STATUS

proposed

editing