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#37 by Alois P. Heinz at Tue Jan 04 21:51:46 EST 2022
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#36 by Jon E. Schoenfield at Tue Jan 04 21:49:41 EST 2022
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#35 by Jon E. Schoenfield at Tue Jan 04 21:49:40 EST 2022
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| NAME
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Odd numbers nk such that the Mersenne number 2^nk - 1 can be written in the form a^2 + 3*b^2.
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| COMMENTS
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These 2^n-k - 1 numbers have no prime factors of the form 2 (mod 3) to an odd power.
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| EXAMPLE
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2^67- - 1 = 10106743618^2+ + 3*3891344499^2 = 9845359982^2+ + 3*4108642899^2
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| EXTENSIONS
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Added 8 more terms - _ from _V. Raman_, Aug 28 2012
Added 6 more terms - _ from _V. Raman_, Aug 29 2012
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| STATUS
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approved
editing
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#34 by N. J. A. Sloane at Fri Jan 18 13:42:11 EST 2019
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| LINKS
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Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/pmain119">/">Factorizations of 2^n-1, for odd n's < 1200</a>
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Discussion
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| Fri Jan 18
| 13:42
| OEIS Server: https://oeis.org/edit/global/2794
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#33 by N. J. A. Sloane at Fri Jan 18 13:38:53 EST 2019
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Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/pmain812pmain119">Factorizations of 2^n-1, for odd n's < 1200</a>
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Discussion
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| Fri Jan 18
| 13:38
| OEIS Server: https://oeis.org/edit/global/2793
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#32 by Russ Cox at Mon Aug 11 22:45:49 EDT 2014
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Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/pmain812">Factorizations of 2^n-1, for odd n's < 1200</a>
Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/pmain812">Factorizations of 2^n-1, for odd n's < 1200</a>
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Discussion
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| Mon Aug 11
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| OEIS Server: https://oeis.org/edit/global/2322
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#31 by Charles R Greathouse IV at Fri Sep 07 02:38:26 EDT 2012
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#30 by Charles R Greathouse IV at Fri Sep 07 02:38:22 EDT 2012
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| NAME
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Odd numbers n such that the Mersenne Numbernumber 2^n - 1 can be written in the form a^2 + 3*b^2.
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| EXTENSIONS
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Added 6 more terms - - _V. Raman, _, Aug 29 2012
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| STATUS
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approved
editing
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#29 by N. J. A. Sloane at Wed Aug 29 12:01:08 EDT 2012
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#28 by V. Raman at Wed Aug 29 11:40:03 EDT 2012
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