A393814 - OEIS

%I #20 Mar 10 2026 16:35:53

%S 1,3,2,11,8,14,26,4,47,92,111,181,150,371,361,781,828,366,19,61,879,

%T 4802,3378,5329,9462,32102,18954,18107,16114,4202,25231,60240,92404,

%U 92188,14804,2426,2405,89386,110522,1814,181464,332551,165179,152564,57504,1355

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

%C 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.

%C 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.

%C A393815 gives corresponding indices.

%H Benjamin Chaffin, <a href="/A393814/b393814.txt">Table of n, a(n) for n = 1..5104</a>

%e 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.

%Y Cf. A005132, A064228, A065052, A393815.

%K nonn

%O 1,2

%A _Benjamin Chaffin_, Feb 28 2026