Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%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