A114890 -id:A114890 - cp's OEIS frontend

A114889 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n)+a(i) is not a power of 3, for i=1,..., n-1.

1, 3, 4, 7, 9, 10, 11, 12, 13, 19, 21, 22, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 55, 57, 58, 61, 63, 64, 65, 66, 67, 73, 75, 76, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108

Offset: 1

John W. Layman, Jan 04 2006

nonn

The differences of {a(n)}, together with a conjectured formula for them, is given in A114890.

			Given that a(1)=1, a(2)=3 and a(3)=4, we find that a(4)>5 since 5+4=9 and a(4)>6 since 6+3=9. But none of 7+1, 7+3, or 7+4 is a power of 3, so a(4)=7.

Cf. A005652, A114890.

A119350 First differences of A118374.

Original entry on oeis.org

1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

John W. Layman, May 23 2006

nonn

Cf. A118374, A114889, A114890.

Conjecture. Define g(1)=1 and, for i>1, g(i)=2*g(i-1)+2^(i-2). Also define h(1)=1, h(2)=4 and, for i>2, h(i)=h(i-1)+2^(i-2). Then a(n)=h(i) if n=g(i), a(n)=1 if g(i)-2^(i-2)<=n

A138684 First differences of A138683.

Original entry on oeis.org

1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 6, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 3, 1, 1, 4, 1

Offset: 1

John W. Layman, Mar 26 2008

nonn

The graph of this sequence is fractal-like.

Conjecture. Let x(1)=1, x(2)=2, x(n) = 2*x(n-1) + x(n-2), and let y(1)=1, y(2)=3, y(n) = y(n-1) + y(n-2). Then if n=x(k), a(n)=y(k); if x(k) < n < 2*x(k), a(n) = a(n-x(k)); and if 2*x(k) <= n < x(k+1), a(n)=1. (This has been confirmed for n < 500.) - John W. Layman, Nov 26 2011

Cf. A114889, A114890, A138683.

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A114889 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n)+a(i) is not a power of 3, for i=1,..., n-1.

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A119350 First differences of A118374.

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A138684 First differences of A138683.

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