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A226389 Triangular numbers representable as triangular(x)*triangular(y)+1. 1
1, 10, 91, 136, 946, 1711, 1891, 5671, 8911, 10585, 11026, 11935, 13861, 19306, 21736, 26335, 32131, 36856, 44551, 49141, 65341, 107416, 138601, 239086, 305371, 351541, 366796, 459361, 849556, 873181, 933661, 1100386, 1413721, 1516411, 1904176, 2297296, 2467531, 3837835 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Cases with x=y are included.

The associated indices in A000217 are 1, 4, 13, 16, 43, 58, 61, 106, 133, 145, 148, 154,...

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000

EXAMPLE

10 = 3 * 3 + 1,

91 = 6 * 15 + 1,

3837835 = 378 * 10153 + 1.

MAPLE

A000217inv:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end proc:

A000217 := proc(n)

    n*(n+1)/2 ;

end proc:

isA226389 := proc(n)

    local Tx, Ty;

    if n = 1 then

        return true;

    elif A000217inv(n) >= 0 then

        for x from 0 do

            Tx := A000217(x) ;

            if Tx+1 > n then

                return false;

            end if;

            for y from 0 to x do

                Ty := A000217(y) ;

                if Tx*Ty+1 >n then

                    break;

                elif Tx*Ty+1 = n then

                    return true;

                end if;

            end do:

        end do:

    else

        false;

    end if;

end proc:

for n from 0 do

    Tn := A000217(n) ;

    if isA226389(Tn) then

        printf("%d, \n", Tn) ;

    end if;

end do: # R. J. Mathar, Jun 06 2013

CROSSREFS

Cf. A000217, A188630, A225390.

Sequence in context: A116348 A043088 A175710 * A119047 A143572 A244203

Adjacent sequences:  A226386 A226387 A226388 * A226390 A226391 A226392

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Jun 06 2013

STATUS

approved

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)