

A080075


Proth numbers: of the form k*2^m + 1 for k odd, m >= 1 and 2^m > k.


10



3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409
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OFFSET

1,1


COMMENTS

a(n) ~ n^2/2.  Thomas Ordowski, Oct 19 2014


LINKS

Charles R Greathouse IV, Table of n, a(n) for n=1,...,10000.
Eric Weisstein's World of Mathematics, Proth Number


FORMULA

a(n) = A116882(n+1)+1.  Klaus Brockhaus, Georgi Guninski and _Maximilian Hasler_, Aug 16 2010
a(n) = A157892(n)*2^A157893(n) + 1. [M. F. Hasler, Aug 16 2010]


PROG

(PARI) isproth(x)={ !bittest(x, 0) & (x>>valuation(x, 2))^2 < x } \\ [M. F. Hasler, Aug 16 2010]


CROSSREFS

Cf. A080076, A112714.
Sequence in context: A211340 A061571 A049690 * A007664 A215812 A114395
Adjacent sequences: A080072 A080073 A080074 * A080076 A080077 A080078


KEYWORD

nonn


AUTHOR

Eric W. Weisstein, Jan 24 2003


STATUS

approved



