A020948 -id:A020948 - cp's OEIS frontend

A020947 Least k such that A(k) = n, where A( ) is sequence A020943.

2, 6, 15, 14, 28, 61, 30, 58, 121, 60, 62, 116, 241, 120, 245, 122, 124, 469, 234, 806, 509, 254, 242, 248, 244, 252, 250, 466, 510, 468, 494, 482, 486, 977, 488, 484, 504, 492, 930, 490, 506, 936, 500, 932, 940, 966

Offset: 1

Clark Kimberling

nonn

Cf. A020943-A020945, A002487, A020948-A020950.

A020943 a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1).

Original entry on oeis.org

0, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 2, 1, 4, 3, 4, 1, 2, 1, 1, 0, 2, 2, 3, 1, 3, 2, 5, 3, 7, 4, 7, 3, 5, 2, 3, 1, 3, 2, 2, 0, 1, 1, 2, 1, 4, 3, 5, 2, 4, 2, 4, 2, 5, 3, 7, 4, 8, 4, 10, 6, 11, 5, 11, 6, 10, 4, 8, 4, 7, 3, 5, 2, 4, 2, 4, 2, 5, 3, 4, 1, 2, 1, 1, 0, 2, 2, 3, 1, 3, 2, 5, 3, 7, 4, 8, 4, 7, 3, 6, 3, 6, 3

Offset: 1

Clark Kimberling

Presumably, the positions n such that a(n)=0 are the terms of A097074. - Ivan Neretin, Jul 06 2015

Ivan Neretin, Table of n, a(n) for n = 1..5461

Cf. A020947, A020948, A020949, A020950.

a = {0, 1, 1}; Do[AppendTo[a, a[[n]] + a[[n - 1]]]; AppendTo[a, Abs[a[[-1]] - a[[-2]]]], {n, 2, 51}]; a (* Ivan Neretin, Jul 06 2015 *)

More terms from Henry Bottomley, May 16 2001

A020944 a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1), a(0) = -1.

Original entry on oeis.org

-1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3

Offset: 0

Clark Kimberling

a(n) = abs(t(n+1)) if n>0 where t(n) is the twisted Stern sequence defined by R. Bacher and M. Coons. - Michael Somos, Jan 08 2011

a(A153893(n)) = 0. - Reinhard Zumkeller, Mar 13 2011

			G.f. = -1 + x + x^3 + x^4 + x^6 + x^7 + 2*x^8 + x^9 + x^10 + x^12 + x^13 + 2*x^14 + ...

Seiichi Manyama, Table of n, a(n) for n = 0..12287
Roland Bacher, Twisting the Stern sequence, arXiv:1005.5627v1 [math.CO], 2010.
Michael Coons, On Some Conjectures concerning Stern's Sequence and its Twist, arXiv:1008.0193v3 [math.NT], 2010.

Cf. A020947, A020948, A020949, A020950, A153893.

a020944 n = a020944_list !! n
a020944_list = -1 : f [1,0] where f (x:y:xs) = x : f (y:xs ++ [x,x+y])
-- Same list generator function as for a020951_list, cf. A020951.
-- Reinhard Zumkeller, Mar 13 2013

a[ n_] := Which[ n < 2, Boole[n == 1] - Boole[n == 0], OddQ[n], Abs[a[n - 1] - a[n - 2]], True, a[n/2] + a[n/2 - 1]]; (* Michael Somos, Jul 25 2018 *)

{a(n) = if( n<2,(n==1) - (n==0),  n%2, abs( a(n-1) - a(n-2) ), a(n/2) + a(n/2 - 1) )}; /* Michael Somos, Jan 08 2011 */

{a(n) = my(A, m); if( n<0, 0, m = 1; A = -1 + O(x); while( m <= n, m*=2; A = 2*x + (1 + x + x^2) * subst( A, x, x^2 ) ); polcoeff( A, n ) )}; /* Michael Somos, Jan 08 2011 */

G.f. A(x) satisfies: A(x) = 2*x + (1 + x + x^2) * A(x^2). - Michael Somos, Jan 08 2011

More terms from Henry Bottomley, May 16 2001

Added a(0) from Michael Somos, Jan 08 2011

cp's OEIS Frontend

A020947 Least k such that A(k) = n, where A( ) is sequence A020943.

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A020943 a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1).

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A020944 a(2n+1) = |a(2n) - a(2n-1)|, a(2n) = a(n) + a(n-1), a(0) = -1.

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