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Proth numbers h*2^k+1, with odd h < 2^k, ordered first by k then by h.
1

%I #66 Feb 16 2024 14:49:43

%S 3,5,13,9,25,41,57,17,49,81,113,145,177,209,241,33,97,161,225,289,353,

%T 417,481,545,609,673,737,801,865,929,993,65,193,321,449,577,705,833,

%U 961,1089,1217,1345,1473,1601,1729,1857,1985,2113,2241,2369,2497,2625,2753,2881

%N Proth numbers h*2^k+1, with odd h < 2^k, ordered first by k then by h.

%H Daniel Sturm, <a href="/A369901/b369901.txt">Table of n, a(n) for n = 1..1023</a>

%H David A. Corneth, <a href="/A369901/a369901.gp.txt">PARI program</a>.

%H E. Proth, <a href="https://www.biodiversitylibrary.org/item/24818#page/932/mode/1up">Théorèmes sur les nombres premiers</a>, Comptes rendus hebdomadaires des séances de l'Académie des sciences, 1878, p. 926.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Proth_prime">Proth Primes</a>.

%F a(2^b+c) = (2c+1)*2^(b+1) for 0 <= c < 2^b.

%e Displayed as an irregular triangle:

%e 3;

%e 5, 13;

%e 9, 25, 41, 57;

%e 17, 49, 81, 113, 145, 177, 209, 241;

%e ...

%o (Python)

%o def A369901(n):

%o b = n.bit_length() - 1

%o c = n - 2**b

%o return (2*c+1)*2**(b+1)+1

%o (PARI) \\ See PARI link

%Y Cf. A080075 (Proth numbers).

%Y Cf. A000051 (1st column), A020515 (right diagonal).

%K nonn,easy,tabf

%O 1,1

%A _Daniel Sturm_, Feb 05 2024

%E More terms from _David A. Corneth_, Feb 05 2024