A378244 a(1) = 1, a(2) = 2, and for any n > 2, a(n) is the least number > a(n-1) that belongs to a unique Fibonacci-like sequence starting with two distinct earlier terms.

1, 2, 4, 7, 10, 13, 25, 30, 39, 42, 54, 57, 98, 101, 119, 122, 134, 150, 165, 174, 183, 202, 224, 229, 247, 264, 295, 311, 326, 347, 382, 391, 399, 413, 472, 475, 503, 520, 543, 566, 583, 617, 669, 675, 728, 734, 848, 859, 959, 976, 1052, 1080, 1099, 1108

Offset

1,2

Comments

This sequence is a variant of Ulam numbers (A002858).

There is only one pair of consecutive terms: a(2) = a(1) + 1 as for any n > 2, a(n)+1 belongs to the two Fibonacci-like sequences starting with (a(1), a(n)) and with (a(n), a(1)).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for Ulam numbers

Rémy Sigrist, C++ program

Example

a(1) = 1 and a(2) = 2 by definition.
a(3) must be > 2 and belong to exactly one of the following sequences:
- 1, 2, 3, 5, 8, etc. (positive Fibonacci numbers),
- 2, 1, 3, 4, 7, etc. (Lucas numbers).
We take a(3) = 4.

Prog

(C++) // See Links section.

Crossrefs

Cf. A002858, A378242.

Sequence in context: A168112 A170894 A151986 * A287522 A101472 A273872

Adjacent sequences: A378241 A378242 A378243 * A378245 A378246 A378247

Keyword

nonn

Author

Rémy Sigrist, Nov 20 2024

Status

approved