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