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A253386 Suffixes of 3991687693967 (left-truncatable prime).

%I A253386 #104 Feb 16 2025 08:33:24
%S A253386 7,67,967,3967,93967,693967,7693967,87693967,687693967,1687693967,
%T A253386 91687693967,991687693967,3991687693967
%N A253386 Suffixes of 3991687693967 (left-truncatable prime).
%C A253386 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 A253386 Mikk Heidemaa, <a href="http://oeis.net16.net">Related material</a> (2015)
%H A253386 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TruncatablePrime.html">Truncatable Prime</a>
%H A253386 Wikipedia, <a href="http://en.wikipedia.org/wiki/Truncatable_prime">Truncatable prime</a>
%H A253386 <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>
%F A253386 a(n) = 3991687693967 mod 10^n for 1 <= n <= 13. - _Mikk Heidemaa_, Oct 07 2017
%e A253386 Triangular form:
%e A253386 ----------------
%e A253386 ............7
%e A253386 ...........67
%e A253386 ..........967*
%e A253386 .........3967
%e A253386 ........93967
%e A253386 .......693967
%e A253386 ......7693967**
%e A253386 .....87693967
%e A253386 ....687693967
%e A253386 ...1687693967
%e A253386 ..91687693967
%e A253386 .991687693967
%e A253386 3991687693967***
%e A253386 ----------------
%e A253386 * None from 3rd row (967,...,3991687693967) cannot be written as a sum of 3 squares.
%e A253386 ** The palindromic prime suffix.
%e A253386 *** a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967;
%e A253386 a=693967; b=93967; c=3967; d=967; e=67; f=7; g=4114278523; h=37; i=27.
%e A253386 a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g * h * i = 3991687693967^5;
%e A253386 a=693967; b=93967; c=3967; d=967; e=67; f=7;
%e A253386 g=3571123727278334614405609468109056139549629; h=228288322626423; i=124339.
%e A253386 (All primes.)
%t A253386 Column[ Table[ Mod[ 3991687693967, 10^n], {n, 13}], Right] (* _Mikk Heidemaa_, Oct 07 2017 *)
%Y A253386 Cf. A012885, A024785, A253427.
%K A253386 nonn,base,fini,full
%O A253386 1,1
%A A253386 _Mikk Heidemaa_, Dec 31 2014