A393814 Minimum value taken by Recamán's sequence (A005132) between terms where A005132(k) mod k increases.

1, 3, 2, 11, 8, 14, 26, 4, 47, 92, 111, 181, 150, 371, 361, 781, 828, 366, 19, 61, 879, 4802, 3378, 5329, 9462, 32102, 18954, 18107, 16114, 4202, 25231, 60240, 92404, 92188, 14804, 2426, 2405, 89386, 110522, 1814, 181464, 332551, 165179, 152564, 57504, 1355

Offset

1,2

Comments

Let R(n) = n-th term of Recamán's sequence (A005132). R(n) can be relatively small when R(n) is close to (but greater than) a multiple of n; that is, (R(n) mod n) is small. The sequence (R(n) mod n) (A065052) is generally nonincreasing until it wraps around to a value close to n. This sequence gives the minimum value of R(n) in each interval between wraparounds; that is, between terms where (R(n) mod n) increases.

These are the points that terminate each downward arc seen in the graph of A005132, and are the places where the Recamán sequence has the best chance of filling in a small missing number. The record values in A064228 (except the initial 0) will appear in this sequence.

A393815 gives corresponding indices.

Links

Benjamin Chaffin, Table of n, a(n) for n = 1..5104

Example

The sixth interval of decreasing values for (R(n) mod n) is between R(22)=41 (41 mod 22 = 19) and R(39)=78 (78 mod 39 = 0). In this interval, the minimum value of R(n) is R(31)=14. Thus a(6) = 14.

Crossrefs

Cf. A005132, A064228, A065052, A393815.

Sequence in context: A276589 A275950 A276587 * A180185 A072634 A086194

Adjacent sequences: A393811 A393812 A393813 * A393815 A393816 A393817

Keyword

nonn

Author

Benjamin Chaffin, Feb 28 2026

Status

approved