A069077 -id:A069077 - cp's OEIS frontend

A061380 Triangular numbers with product of digits also a triangular number.

0, 1, 3, 6, 10, 66, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1326, 1540, 1770, 1830, 2016, 2080, 2556, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 5671, 6105

Offset: 1

Amarnath Murthy, May 02 2001

			153 is a triangular number and the product of digits 15 is also a triangular number.

Michel Marcus, Table of n, a(n) for n = 1..10000

Cf. A000217, A061867, A069077, A117710.

[t: n in [0..110] | IsSquare(8*p+1) where p is &*Intseq(t) where t is (n*(n+1) div 2)];  // Bruno Berselli, Jun 30 2011

q:= n-> (l-> issqr(1+8*mul(i,i=l)))(convert(n, base, 10)):
select(q, [seq(i*(i+1)/2, i=0..110)])[];  # Alois P. Heinz, Mar 17 2023

tn=Table[n (n+1)/2, {n, 0, 110}] ;Select[tn,MemberQ[tn,Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)

isok(k) = ispolygonal(k, 3) && ispolygonal(vecprod(digits(k)), 3); \\ Michel Marcus, Mar 17 2023

More terms from Erich Friedman, May 08 2001

Offset 1 from Michel Marcus, Mar 17 2023

A285079 Oblong numbers the product of whose digits are positive oblong numbers.

Original entry on oeis.org

2, 6, 12, 56, 132, 156, 756, 2756, 4556, 6162, 6972, 7656, 13572, 21756, 31152, 33672, 45156, 61752, 84972, 153272, 166872, 279312, 467172, 626472, 661782, 1273512, 1412532, 1541322, 1568756, 1596432, 1786232, 1867322, 2678132, 2817362, 3416952, 3521252

Offset: 1

Melvin Peralta, Apr 09 2017

Oblong numbers are numbers of the form k*(k+1) (A002378).

Robert Israel and Giovanni Resta, Table of n, a(n) for n = 1..391 (terms < 10^25, first 221 terms from Robert Israel)

Cf. A002378, A053059, A069077.

filter:= proc(x) local t; t:= convert(convert(x,base,10),`*`);
t > 0 and issqr(1+4*t); end proc:
select(filter, [seq(x*(1+x),x=1..10^4)]); # Robert Israel, Apr 14 2017

f[x_] := Sqrt[1 + 4 (Times @@ IntegerDigits[x])]; Select[Table[n (n + 1), {n, 1, 10000}], f[#] > 1 && Mod[f[#], 2] == 1 &]

cp's OEIS Frontend

A061380 Triangular numbers with product of digits also a triangular number.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Extensions