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.

 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

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.

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