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A227220

Smallest triangular number ending in n 6's.

6, 66, 666, 8146666, 2340066666, 109704666666, 15212926666666, 66488766666666, 173147535666666666, 11302559226666666666, 14642337066666666666, 77850029701666666666666, 1029964845546666666666666, 3086210323568466666666666666, 4014564887872666666666666666

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OFFSET

1,1

COMMENTS

If a triangular number ends in like digits then it can only end in 0's, 1's, 5's or 6's.

LINKS

Robert Israel, Table of n, a(n) for n = 1..500

EXAMPLE

a(4)=8146666 because 8146666 is the smallest triangular number ending in 4 '6's.

MAPLE

f:= proc(n) local k;

k:=min(map(rhs@op, [msolve(k*(k+1)=4/3*(10^n-1), 2*10^n)]));

k*(k+1)/2

end proc:

map(f, [$1..30]); # Robert Israel, Sep 04 2019

MATHEMATICA

t = {}; Do[Do[x = n*(n + 1)/2; If[Mod[x, 10^m] == 6*(10^m - 1)/9, AppendTo[t, x]; Break[]], {n, 1, 10^m}], {m, 1, 10}]; t

a[n_] := Block[{x, y, s}, s = y /. List@ ToRules[ Reduce[(y+1)* y/2 == x*10^n + 2(10^n - 1)/3 && y > 0 && x >= 0, {y, x}, Integers] /. C[1] -> 0]; Min[s*(s + 1)/2]]; Array[a, 20] (* Giovanni Resta, Sep 20 2013 *)

PROG

(Python)

from sympy import sqrt_mod_iter

def A227220(n):

k, a = 10**n<<1, (10**n-1)//3<<2

m = (a<<2)+1

return min(b for b in ((d>>1)*((d>>1)+1) for d in sqrt_mod_iter(m, k) if d&1) if b%k==a)>>1 # Chai Wah Wu, May 04 2024

CROSSREFS

Cf. A000217, A187127, A227218, A227219.

Sequence in context: A112902 A119160 A119210 * A119234 A119232 A186675

Adjacent sequences: A227217 A227218 A227219 * A227221 A227222 A227223

KEYWORD