A253386 Suffixes of 3991687693967 (left-truncatable prime).

7, 67, 967, 3967, 93967, 693967, 7693967, 87693967, 687693967, 1687693967, 91687693967, 991687693967, 3991687693967

Offset

1,1

Comments

3991687693967 (13 digits) includes the longest (7 digits) palindromic prime suffix (7693967) among the left-truncatable primes (digit '0' excluded). The largest one (24 digits, see A253427) contains a nonprime palindrome of 7 digits (1264621). The terms from a(3) to a(13) cannot be written as a sum of 3 squares.

Links

Table of n, a(n) for n=1..13.

Mikk Heidemaa, Related material (2015)

Eric Weisstein's World of Mathematics, Truncatable Prime

Wikipedia, Truncatable prime

Index entries for sequences related to truncatable primes

Formula

a(n) = 3991687693967 mod 10^n for 1 <= n <= 13. - Mikk Heidemaa, Oct 07 2017

Example

Triangular form:
----------------
............7
...........67
..........967*
.........3967
........93967
.......693967
......7693967**
.....87693967
....687693967
...1687693967
..91687693967
.991687693967
3991687693967***
----------------
* None from 3rd row (967,...,3991687693967) cannot be written as a sum of 3 squares.
** The palindromic prime suffix.
*** a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967;
a=693967; b=93967; c=3967; d=967; e=67; f=7; g=4114278523; h=37; i=27.
a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967^5;
a=693967; b=93967; c=3967; d=967; e=67; f=7;
g=3571123727278334614405609468109056139549629; h=228288322626423; i=124339.
(All primes.)

Mathematica

Column[ Table[ Mod[ 3991687693967, 10^n], {n, 13}], Right] (* Mikk Heidemaa, Oct 07 2017 *)

Crossrefs

Cf. A012885, A024785, A253427.

Sequence in context: A364924 A082578 A291814 * A082698 A182127 A093170

Adjacent sequences: A253383 A253384 A253385 * A253387 A253388 A253389

Keyword

nonn,base,fini,full

Author

Mikk Heidemaa, Dec 31 2014

Status

approved