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A227220 Smallest triangular number ending in n 6's. 3
6, 66, 666, 8146666, 2340066666, 109704666666, 15212926666666, 66488766666666, 173147535666666666, 11302559226666666666, 14642337066666666666, 77850029701666666666666, 1029964845546666666666666, 3086210323568466666666666666, 4014564887872666666666666666 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Cf. A000217, A187127, A227218, A227219.

Sequence in context: A112902 A119160 A119210 * A119234 A119232 A186675

Adjacent sequences:  A227217 A227218 A227219 * A227221 A227222 A227223

KEYWORD

nonn,base

AUTHOR

Shyam Sunder Gupta, Sep 19 2013

EXTENSIONS

a(11)-a(15) from Giovanni Resta, Sep 20 2013

STATUS

approved

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Last modified September 20 08:53 EDT 2021. Contains 347579 sequences. (Running on oeis4.)