A012885 Suffixes of 357686312646216567629137 (all primes).

7, 37, 137, 9137, 29137, 629137, 7629137, 67629137, 567629137, 6567629137, 16567629137, 216567629137, 6216567629137, 46216567629137, 646216567629137, 2646216567629137, 12646216567629137, 312646216567629137, 6312646216567629137, 86312646216567629137

Offset: 1

Author

Larry Calmer (larry(AT)wri.com), Simon Plouffe

Keywords

• nonn
• fini
• full
• base

Comments

From Mikk Heidemaa, Mar 23 2015: (Start)

a(2),...,a(24) all have a single representation (in positive integers) as the sum of two squares (e.g., a(24) = 416865370156^2 + 428846797599^2) and as the hypotenuse of a primitive Pythagorean triple (357686312646216567629137^2 = 10132838975618776700465^2 + 357542758042644694110888^2).

---

a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 357686312646216567629137^2;

a=304233682432674451033719; b=185074861663432734470527;

c=4189176178164916432878; d=33333333333333333333333; e=3333333; f=3.

---

a^2 + b^2 + c^2 + d^2 + e^2 + f^2 = 357686312646216567629137^3;

a=210197737649788368191109924028342434;

b=39738123500625252940689952285037741;

c=777777777777777777777777;

d=777777777777777777777777;

e=777777777777777777;

f=777777777777.

a=170350493188466620042802284807886346;

b=129394423538599186274382140531063939;

c=777777777777777777777777;

d=777777777777777777777777;

e=777777777777777777;

f=777777777777.

---

x^2 + y^2 = 357686312646216567629137^3;

x=144701758632763782416276428525674993;

y=157555096461604743754426503960480452;

x=149107037120999813337660002835835372;

y=153392629723324670471173010334042063.

(End)

Examples

			.......................7
......................37
.....................137
....................9137
...................29137
..................629137
.................7629137
................67629137
...............567629137
..............6567629137
.............16567629137
............216567629137
...........6216567629137
..........46216567629137
.........646216567629137
........2646216567629137
.......12646216567629137
......312646216567629137
.....6312646216567629137
....86312646216567629137
...686312646216567629137
..7686312646216567629137
.57686312646216567629137
357686312646216567629137
------------------------
		

Links

• Mikk Heidemaa, Table of n, a(n) for n = 1..24
• James Grime and Brady Haran, 357686312646216567629137, Numberphile video (2018).
• Miguel A. Martin-Delgado, Chiral Prime Concatenations, arXiv:2009.12305 [math.NT], 2020.

Crossrefs

Cf. A024785.

Programs

Mathematica

Table[Mod[357686312646216567629137,10^n] ,{n, 1, 24}] (* José de Jesús Camacho Medina, Dec 21 2016 *)

Formula

a(n) = 357686312646216567629137 mod 10^n. - José de Jesús Camacho Medina, Dec 21 2016