A306829 a(1) = 1; a(n+1) is the smallest k > a(n) such that 2^k == 2^a(n) (mod a(n)).

1, 2, 3, 5, 9, 15, 19, 37, 73, 82, 102, 110, 130, 142, 177, 235, 327, 363, 473, 543, 723, 747, 993, 1023, 1033, 1291, 2581, 2889, 3843, 3903, 5203, 5973, 6153, 7029, 7239, 7365, 8345, 10013, 10373, 10593, 12183, 12313, 13192, 13240, 13300, 13480, 13564, 13677

Offset

1,2

Comments

The number of consecutive terms with the same parity: 1, 1, 7, 5, 28, 5, 16, 13, 47, 4, 70, 6, 56, 4, 32, 11, 17, 21, 22, 11, 2, 20, 67, 13, 22, 36, 8, 9,101, 47, 24, 4, 1, 7, 2, 79, 20, 71, 47, 92, 36, 57, 90, 38, 167, 215, 31, 17, 62, ... i.e.; 1 odd term, 1 even term, 7 odd terms, 5 even terms, 28 odd terms, 5 even terms, ...

Links

Robert Israel, Table of n, a(n) for n = 1..3000

Formula

a(n+1) = a(n) + ord_{A000265(a(n))}(2), where A000265(m) is the odd part of m.

Maple

A[1]:= 1:
for n from 2 to 100 do A[n]:= A[n-1] + numtheory:-order(2, A[n-1]/2^padic:-ordp(A[n-1], 2)) od:
seq(A[n], n=1..100); # Robert Israel, Apr 10 2019

Prog

(PARI) odd(n) = n >> valuation(n, 2);
lista(nn) = {a = 1; print1(a, ", "); for (n=2, nn, a = a + znorder(Mod(2, odd(a))); print1(a, ", "); ); } \\ Michel Marcus, Mar 23 2019

Crossrefs

Cf. A000265, A002326.

Sequence in context: A101461 A085897 A361906 * A067798 A205536 A281704

Adjacent sequences: A306826 A306827 A306828 * A306830 A306831 A306832

Keyword

nonn

Author

Thomas Ordowski, Mar 12 2019

Extensions

More terms from Amiram Eldar, Mar 12 2019

Status

approved