A308721 -id:A308721 - cp's OEIS frontend

A333210 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 2, 1, 0, 6, 0, 1, 3, 8, 0, 0, 18, 0, 1, 7, 5, 0, 0, 7, 0, 1, 7, 7, 0, 4, 17, 0, 0, 10, 0, 1, 10, 23, 0, 0, 7, 12, 0, 22, 0, 1, 10, 10, 0, 14, 22, 0, 7, 12, 12, 0, 13, 0, 1, 13, 10, 22, 0, 11, 17, 0, 34, 0, 1, 10, 6, 0, 61, 0, 1, 6, 23, 0, 17, 13, 0, 23, 4, 0, 54, 0, 1, 12

Offset: 1

Scott R. Shannon, Mar 11 2020

nonn

After 100 million terms the smallest number not appearing is 381884, while the smallest sum of adjacent terms not appearing is 487833.

			a(3) = 0 as a(1)+a(2) = 0+0 = 0, which has not previously appeared as the sum of two adjacent terms.
a(4) = 1 as a(2)+a(3) = 0+0 = 0, which equals the sum a(1)+a(2), one term back from a(3).
a(5) = 0 as a(3)+a(4) = 0+1 = 1, which has not previously appeared as the sum of two adjacent terms.
a(6) = 1 as a(4)+a(5) = 1+0 = 1, which equals the sum a(3)+a(4), one term back from a(5).
a(19) = 8 as a(17)+a(18) = 1+3 = 4, which equals the sum a(9)+a(10), eight terms back from a(18).

Scott R. Shannon, Table of n, a(n) for n = 1..10000.
Brady Haran and N. J. A. Sloane, Don't Know (the Van Eck Sequence), Numberphile video (2019).

Cf. A181391, A171898, A308721, A333211.

A333211 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)a(n-m) = a(n-1)a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

Original entry on oeis.org

0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 1, 3, 0, 3, 1, 3, 1, 1, 13, 0, 6, 1, 0, 2, 1, 14, 0, 3, 1, 12, 0, 3, 1, 4, 0, 3, 1, 4, 4, 0, 4, 1, 4, 1, 1, 27, 0, 6, 1, 27, 4, 0, 4, 1, 10, 0, 3, 1, 21, 0, 3, 1, 4, 9, 0, 4, 1, 4, 1, 1, 25, 0, 6, 1, 25, 4, 0, 4, 1, 10, 25

Offset: 1

Scott R. Shannon, Mar 11 2020

nonn

After 100 million terms the smallest number not appearing is 179549, while the smallest product of adjacent terms not appearing is 2969.

			a(3) = 0 as a(1)*a(2) = 0*0 = 0, which has not previously appeared as the product of two adjacent terms.
a(4) = 1 as a(2)*a(3) = 0*0 = 0, which equals the product a(1)*a(2), one term back from a(3).
a(5) = 1 as a(3)*a(4) = 0*1 = 0, which equals the product a(2)*a(3), one term back from a(3).
a(6) = 0 as a(4)*a(5) = 1*1 = 1, which has not previously appeared as the product of two adjacent terms.
a(19) = 13 as a(17)*a(18) = 1*1 = 1, which equals the product a(4)*a(5), thirteen terms back from a(18).

Scott R. Shannon, Table of n, a(n) for n = 1..10000.
Brady Haran and N. J. A. Sloane, Don't Know (the Van Eck Sequence), Numberphile video (2019).

Cf. A181391, A171898, A308721, A333210.

cp's OEIS Frontend

A333210 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

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A333211 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)a(n-m) = a(n-1)a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

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cp's OEIS Frontend

A333210 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)+a(n-m) = a(n-1)+a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

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A333211 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)*a(n-m) = a(n-1)*a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.

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A333211 Variation of Van Eck's sequence A181391: a(n+1) = the minimum positive offset m from a(n) such that a(n-m-1)a(n-m) = a(n-1)a(n); a(n+1)=0 if no such m exists. Start with a(1) = a(2) = 0.