A178253 -id:A178253 - cp's OEIS frontend

A178373 a(n) = A001969(n)^A178253(n).

81, 25, 1296, 81, 100, 20736, 50625, 289, 324, 400, 529, 331776, 14348907, 841, 810000, 1089, 1156, 1296, 1521, 1600, 1849, 91125, 2116, 5308416, 2601, 7890481, 459165024, 601692057, 3364, 12960000, 15752961, 4225, 4356, 4624, 5041, 5184

Offset: 1

Jeremy Gardiner, May 26 2010

a(n) is in A000069 for all n.

Since A001969(n) = 2*n + A010060(n) it follows that this sequence has the same parity as A010060.

			A001969(1)=3, A178253(1)=4, a(1)=3^4=81.

Cf. A000069, A001969, A010060, A178253.

a(n)=my(e=2*n--+hammingweight(n)%2, m=1); e>>=valuation(e, 2);  while(hammingweight(e^m++)%2==0, ); e^m \\ Charles R Greathouse IV, Mar 22 2013

A178307 Remove powers of 2 from A000069. Let b(n) be n-th term of the remaining sequence. Then a(n) is the least number m such that (b(n))^m is in A001969.

Original entry on oeis.org

3, 3, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 2, 3, 3, 2, 3, 2, 4, 4, 2, 3, 3, 5, 2, 3, 4, 2, 4, 2, 2, 3, 4, 2, 3, 2, 3, 3, 3, 2, 2, 4, 4, 4, 9, 2, 2, 2, 3, 3, 2, 4, 5, 3, 2, 3, 3, 4, 2, 4, 2, 2, 4, 3, 3, 2, 2, 2, 3, 2, 4, 4, 2, 2, 3, 4, 2, 2, 4, 3, 3, 4, 5, 3, 5, 2, 2, 2, 6, 4, 4, 2, 4, 2, 2, 9, 2, 2, 2, 2, 3, 2, 3, 3, 3

Offset: 1

Vladimir Shevelev, May 24 2010, May 25 2010

nonn

The sequence {b(n)} coincides with A075930. Conjecture. For every n>=1, a(n) does exist.

The sequence b(n) is A075930 (Positions of check bits in code in A075928); see comment in that sequence. [From Jeremy Gardiner, May 26 2010]

Cf. A000069 A001969 A178253

Cf. A075930. [From Jeremy Gardiner, May 26 2010]

If k=b(n)=2^m*b(s), where b(s) is odd, then a(n)=a(s).

Edited by N. J. A. Sloane, May 29 2010

Extended by Jeremy Gardiner, May 26 2010

cp's OEIS Frontend

A178373 a(n) = A001969(n)^A178253(n).

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