A369901 Proth numbers h*2^k+1, with odd h < 2^k, ordered first by k then by h.
3, 5, 13, 9, 25, 41, 57, 17, 49, 81, 113, 145, 177, 209, 241, 33, 97, 161, 225, 289, 353, 417, 481, 545, 609, 673, 737, 801, 865, 929, 993, 65, 193, 321, 449, 577, 705, 833, 961, 1089, 1217, 1345, 1473, 1601, 1729, 1857, 1985, 2113, 2241, 2369, 2497, 2625, 2753, 2881
Offset: 1
Examples
Displayed as an irregular triangle: 3; 5, 13; 9, 25, 41, 57; 17, 49, 81, 113, 145, 177, 209, 241; ...
Links
- Daniel Sturm, Table of n, a(n) for n = 1..1023
- David A. Corneth, PARI program.
- E. Proth, Théorèmes sur les nombres premiers, Comptes rendus hebdomadaires des séances de l'Académie des sciences, 1878, p. 926.
- Wikipedia, Proth Primes.
Programs
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PARI
\\ See PARI link
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Python
def A369901(n): b = n.bit_length() - 1 c = n - 2**b return (2*c+1)*2**(b+1)+1
Formula
a(2^b+c) = (2c+1)*2^(b+1)+1 for 0 <= c < 2^b. [Corrected by Thomas Ordowski, Aug 11 2025]
a(n) = (2n+1-2^m)*2^m+1 = (2n+1)*2^m-4^m+1, where m = floor(log_2(2n+1)). - Thomas Ordowski, Aug 11 2025
Extensions
More terms from David A. Corneth, Feb 05 2024