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Suffixes of 3991687693967 (left-truncatable prime).
1

%I #103 Oct 09 2017 02:17:01

%S 7,67,967,3967,93967,693967,7693967,87693967,687693967,1687693967,

%T 91687693967,991687693967,3991687693967

%N Suffixes of 3991687693967 (left-truncatable prime).

%C 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.

%H Mikk Heidemaa, <a href="http://oeis.net16.net">Related material</a> (2015)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TruncatablePrime.html">Truncatable Prime</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Truncatable_prime">Truncatable prime</a>

%H <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>

%F a(n) = 3991687693967 mod 10^n for 1 <= n <= 13. - _Mikk Heidemaa_, Oct 07 2017

%e Triangular form:

%e ----------------

%e ............7

%e ...........67

%e ..........967*

%e .........3967

%e ........93967

%e .......693967

%e ......7693967**

%e .....87693967

%e ....687693967

%e ...1687693967

%e ..91687693967

%e .991687693967

%e 3991687693967***

%e ----------------

%e * None from 3rd row (967,...,3991687693967) cannot be written as a sum of 3 squares.

%e ** The palindromic prime suffix.

%e *** a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967;

%e a=693967; b=93967; c=3967; d=967; e=67; f=7; g=4114278523; h=37; i=27.

%e a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967^5;

%e a=693967; b=93967; c=3967; d=967; e=67; f=7;

%e g=3571123727278334614405609468109056139549629; h=228288322626423; i=124339.

%e (All primes.)

%t Column[ Table[ Mod[ 3991687693967, 10^n], {n, 13}], Right] (* _Mikk Heidemaa_, Oct 07 2017 *)

%Y Cf. A012885, A024785, A253427.

%K nonn,base,fini,full

%O 1,1

%A _Mikk Heidemaa_, Dec 31 2014