A087345 Smallest prime which is a concatenation of n successive triangular numbers, or 0 if no such number exists.

3, 13, 210231253, 171190210231, 36101521, 136101521, 1596165317111770183018911953, 105120136153171190210231, 0, 17020172051739117578177661795518145183361852818721

Offset

1,1

Comments

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..65

Example

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

Maple

ccat:= proc(L) local r, x;
  r:= L[1];
  for x in L[2..-1] do
    r:= r*10^(1+ilog10(x))+x
  od:
  r
end proc:
f:= proc(n) local k, j, t;
    if n mod 9 = 0 then return 0 fi;
    for k from 1 do
      t:= ccat([seq(j*(j+1)/2, j=k..k+n-1)]);
      if isprime(t) then return t fi
    od
end proc:
map(f, [$1..20]); # _Robert Israel_, Mar 13 2018

Crossrefs

Cf. A087344.

Sequence in context: A092830 A317481 A271393 * A048756 A174211 A264611

Adjacent sequences: A087342 A087343 A087344 * A087346 A087347 A087348

Keyword

base,nonn

Author

_Amarnath Murthy_, Sep 06 2003

Extensions

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

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

Status

approved