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Search: id:A055438
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| 101, 402, 903, 1604, 2505, 3606, 4907, 6408, 8109, 10010, 12111, 14412, 16913, 19614, 22515, 25616, 28917, 32418, 36119, 40020, 44121, 48422, 52923, 57624, 62525, 67626, 72927, 78428, 84129, 90030, 96131, 102432, 108933, 115634, 122535
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OFFSET
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1,1
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COMMENT
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For all terms, the first digit is the square of the last digit. Example: 101, 1^2=1; 402, 2^2=4; 903, 3^2=9; 1604, 4^2=16; 44121, 21^2=441 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
If A=[A055438] 100*n.^2+n (101, 402, 903,. ,.,); Y=[A010859] 20 (20, 20, 20,. ,.,); X=[A157956] 200*n+1 (201, 401, 601, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 201^2-101 *20^2=1; 401^2-402*20^2=1; 601^2-903*20^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
If A=[A055438] 100*n.^2+n (101, 402, 903, ,..,); Y=[A157663] 8000*n+40 (8040, 16040, 24040,..,); X=[A157664] 80000*n^2+800*n+1 (80801, 321601, 722401,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 80801^2-101*8040^2=1; 321601^2-402*16040^2=1; 722401^2-903*24040^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tinit), Mar 04 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tinit), Mar 04 2009]
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CROSSREFS
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Cf. A002378, A055437, a(n)=A055436(n) if 10<=n<100.
Different from A031698.
Cf. A157956, A010859 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009]
Cf. A157663, A157664 [From Vincenzo Librandi (vincenzo.librandi(AT)tinit), Mar 04 2009]
Sequence in context: A158192 A062800 A031698 this_sequence A142692 A060012 A142507
Adjacent sequences: A055435 A055436 A055437 this_sequence A055439 A055440 A055441
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 18 2000
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