## Triangular numbers that remain triangular when you add 1 to each of their digits

$10 \; = \; T_4$
$21 \; = \; T_6$

$120 \; = \; T_{15}$
$231 \; = \; T_{21}$

$630 \; = \; T_{35}$
$741 \; = \; T_{38}$

$4560 \; = \; T_{95}$
$5671 \; = \; T_{106}$

$31375 \; = \; T_{250}$
$42486 \; = \; T_{291}$

Find more examples.

math grad - Interest: Number theory
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### 2 Responses to Triangular numbers that remain triangular when you add 1 to each of their digits

1. Steve Kass says:

At first, I could only find three more, but then I found
$268116633060 \; = \; T_{732279}$
$379227744171 \; = \; T_{870893}$

$352237844115 \; = \; T_{839330}$
$463348955226 \; = \; T_{962651}$

$466332185385 \; = \; T_{965745}$
$577443296496 \; = \; T_{1074656}$

$767375280675 \; = \; T_{1238850}$
$878486391786 \; = \; T_{1325508}$

The list goes on, too.

2. paul says:

Here are a few more

{858547217010,
969658328121}

{145320270736742640,
256431381847853751}

{154811284773224745,
265922395884335856}

{248267365358007115,
359378476469118226}

{281460477738830820,
392571588849941931}

{283744366531414440,
394855477642525551}

{420102670183383435,
531213781294494546}

Paul.