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A369901
Proth numbers h*2^k+1, with odd h < 2^k, ordered first by k then by h.
1
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
1,1
LINKS
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.
FORMULA
a(2^b+c) = (2c+1)*2^(b+1) for 0 <= c < 2^b.
EXAMPLE
Displayed as an irregular triangle:
3;
5, 13;
9, 25, 41, 57;
17, 49, 81, 113, 145, 177, 209, 241;
...
PROG
(Python)
def A369901(n):
b = n.bit_length() - 1
c = n - 2**b
return (2*c+1)*2**(b+1)+1
(PARI) \\ See PARI link
CROSSREFS
Cf. A080075 (Proth numbers).
Cf. A000051 (1st column), A020515 (right diagonal).
Sequence in context: A348744 A263829 A028268 * A171424 A231897 A260416
KEYWORD
nonn,easy,tabf
AUTHOR
Daniel Sturm, Feb 05 2024
EXTENSIONS
More terms from David A. Corneth, Feb 05 2024
STATUS
approved