A100250 -id:A100250 - cp's OEIS frontend

A100143 Unique sequence with a(1)=1 where each a(n) occurs in the same order a(n) times consecutively in its sequence of first differences which contains no other terms.

1, 2, 4, 6, 10, 14, 18, 22, 28, 34, 40, 46, 52, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 172, 186, 200, 214, 228, 242, 256, 270, 284, 298, 312, 326, 340, 354, 372, 390, 408, 426, 444, 462, 480, 498, 516, 534, 552, 570, 588, 606, 624, 642, 660, 678, 700

Offset: 1

Rick L. Shepherd, Nov 09 2004

nonn

By definition, for each n the sequence contains exactly one arithmetic progression (beginning at the A100250(n)-th term) of length a(n)+1 with common difference a(n). Contrast with A075349 and its sequence of first differences, A002024, which includes each A075349(n) term A075349(n) times but also includes terms that are not found in A075349.

Cf. A100144 (first differences), A001462 (Golomb's sequence), A075349, A002024.

A100144 First differences of A100143.

Original entry on oeis.org

1, 2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset: 1

Rick L. Shepherd, Nov 09 2004

nonn

Each term a(n) occurs a(n) times consecutively. If duplicate terms are removed, this sequence is equivalent to A100143.

The position where values change, but also the second partial sums are in A100250. - Ralf Stephan, Aug 28 2013

Cf. A100143, A005041.

cp's OEIS Frontend

A100143 Unique sequence with a(1)=1 where each a(n) occurs in the same order a(n) times consecutively in its sequence of first differences which contains no other terms.

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