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A306829 a(1) = 1; a(n+1) is the smallest k > a(n) such that 2^k == 2^a(n) (mod a(n)). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A026008 A101461 A085897 * 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

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)