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Smallest prime which is a concatenation of n successive triangular numbers, or 0 if no such number exists.
2

%I #13 Mar 13 2018 04:17:57

%S 3,13,210231253,171190210231,36101521,136101521,

%T 1596165317111770183018911953,105120136153171190210231,0,

%U 17020172051739117578177661795518145183361852818721

%N Smallest prime which is a concatenation of n successive triangular numbers, or 0 if no such number exists.

%C a(9k) = 0 because the concatenation of 9k successive triangular numbers is always divisible by 3. - _David Wasserman_, May 10 2005

%C a(66) > 10^999 if it is not 0.- _Robert Israel_, Mar 13 2018

%H Robert Israel, <a href="/A087345/b087345.txt">Table of n, a(n) for n = 1..65</a>

%e a(3)=210231253 because 210231253 is the smallest prime formed by concatenation of 3 consecutive triangular numbers i.e. 210,231 and 253.

%p ccat:= proc(L) local r,x;

%p r:= L[1];

%p for x in L[2..-1] do

%p r:= r*10^(1+ilog10(x))+x

%p od:

%p r

%p end proc:

%p f:= proc(n) local k,j,t;

%p if n mod 9 = 0 then return 0 fi;

%p for k from 1 do

%p t:= ccat([seq(j*(j+1)/2,j=k..k+n-1)]);

%p if isprime(t) then return t fi

%p od

%p end proc:

%p map(f, [$1..20]); # _Robert Israel_, Mar 13 2018

%Y Cf. A087344.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Sep 06 2003

%E Corrected and extended by _Shyam Sunder Gupta_, Apr 25 2005 and _David Wasserman_, May 10 2005

%E Edited by _N. J. A. Sloane_, Sep 02 2010