美しい整数の世界 (780ﾚｽ)
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759: １３２人目の素数さん [age] 2024/11/28(木) 19:32:06.58 ID:tl42a9XE(1/7) AAS
table[floor[(1/4){((-1)^n+5√2) (1+√2)^(2floor[(n+1)/2])}],{n,1,10}]

{8, 11, 51, 68, 300, 399, 1751, 2328,
10208, 13571}

三数
(x-3,x+4,sqrt[2x^2+2x+25])

table[sqrt[2x^2+2x+25]],{x,1,10}]

x^2-6x+9
x^2+8x+16
2x^2+2x+25

x^2-2x+9 ベース

4(-1)^(2mod a+1) 1,0,0

-4,x4,+4
2^2,2^3,2^1
2^1,2^2,2^0

2^(a+1)

2,2^3,2^1

113
222
31

0,+1,-1

-2^a

x^2-3(2x)+9
x^2+4(2x)+16
2x^2+2x+25

-3,4,1

table[sqrt[2x(x+1)+25],{x,1,10}]

x(x-6)+9
x(x+8)+16
2x(x+1)+25

{9,16,25} 　　　？

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760: １３２人目の素数さん [age] 2024/11/28(木) 19:33:11.53 ID:tl42a9XE(2/7) AAS
2^(4mod a)x(x+1+7(3mod a)-
7C(0,7mod a))+(a+2)^2

4(-1)^C(0,7mod a) 1,0,0

4(-1)(7mod a)　0,1,1

C(0,4mod a) 1,1,0
C(0,7mod a) 1,0,0

2^(4mod a)x(x+1+7(3mod a))+(a+2)^2

(a+2)^2

table[sqrt[2^(4mod a)floor[(1/4)
{((-1)^n+5√2)(1+√2)^(2floor[(n+1)/2])}]^2+2floor[(1/4)
{((-1)^n+5√2)(1+√2)^(2floor[(n+1)/2])}]
+(a+2)^2],{n,1,10},{a,1,3}]

不完全

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761: １３２人目の素数さん [age] 2024/11/28(木) 20:42:32.61 ID:tl42a9XE(3/7) AAS
(a+3) →4,5,6

(7mod (a+3)) →3,2,1
2(3mod a) →0,2,0

{(7mod (a+3))+2(3mod a)}
→3,4,1

(-1)^C(0,2mod (a+1))
→-1,1,1

x^2-6x+9
x^2+8x+16
2x^2+2x+25

table[2(-1)^C(0,2mod (a+1)){(7mod (a+3))+2(3mod a)},{a,1,3}]

{-6, 8, 2}

★★

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762: １３２人目の素数さん [age] 2024/11/28(木) 21:18:42.36 ID:tl42a9XE(4/7) AAS
◆原始ピタゴラス数y=x+7
直角を挟む2辺

table[floor[(1/4){((-1)^n+5√2) (1+√2)^(2floor[(n+1)/2])}]+a(-1)^a,{n,1,30},{a,3,4}]

{{5, 12}, {8, 15}, {48, 55}, {65, 72},
{297, 304}, {396, 403}, {1748, 1755},
{2325, 2332}, {10205, 10212},
{13568, 13575}, {59496, 59503},
{79097, 79104}, {346785, 346792},
{461028, 461035}, {2021228, 2021235}, {2687085, 2687092}, {11780597, 11780604},
{15661496, 15661503}, {68662368, 68662375},
{91281905, 91281912}, {400193625, 400193632},
{532029948, 532029955}, {2332499396, 2332499403},
{3100897797, 3100897804},
{13594802765, 13594802772},
{18073356848, 18073356855},
{79236317208, 79236317215},
{105339243305, 105339243312},
{461823100497, 461823100504},
{613962102996, 613962103003}}

★

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763: １３２人目の素数さん [age] 2024/11/28(木) 21:41:07.92 ID:tl42a9XE(5/7) AAS
◆斜辺

table[sqrt[2floor[(1/4)
{((-1)^n+5√2)(1+√2)^(2floor[(n+1)/2])}]^2+2floor[(1/4)
{((-1)^n+5√2)(1+√2)^(2floor[(n+1)/2])}]
+25],{n,1,30}]

{13, 17, 73, 97, 425, 565, 2477, 3293,
14437, 19193, 84145, 111865, 490433,
651997, 2858453, 3800117, 16660285,
22148705, 97103257, 129092113,
565959257, 752403973, 3298652285,
4385331725, 19225954453,
25559586377, 112057074433,
148972186537, 653116492145,
868273532845}

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764: １３２人目の素数さん [age] 2024/11/28(木) 21:44:05.34 ID:tl42a9XE(6/7) AAS
オンライン整数列大辞典 A060569

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765: １３２人目の素数さん [age] 2024/11/28(木) 21:52:15.50 ID:tl42a9XE(7/7) AAS
613962102996^2+613962103003^2
-868273532845^2=0

★

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