A375118 Let {b(m)} be Recamán's sequence A005132, with the additional term b(-1):=0. Define a(n) to be the first index m where b(m-1)-m = -n, or -1 if b(m-1)-m never equals -n.

0, 1, 181695, 5, 1523, 137, 15, 1525, 139, 17, 1527, 141, 28, 1529, 143, 30, 1531, 145, 32, 1533, 147, 53, 1535, 149, 55, 1537, 151, 57, 1539, 153, 59, 1541, 155, 61, 1543, 157, 63, 1545, 159, 65, 1547, 161, 276, 1549, 163, 278, 1551, 165, 280, 1553, 167, 282

Offset

0,3

Comments

This sequence is interesting because of the spike at the 2nd term.

The next similar spike occurs at a(59)=181733.

Links

Table of n, a(n) for n=0..51.

Example

Recamán's sequence {b(m)} begins with 0, 1, 3, 6, 2, 7, 13,...
b(1-1)-1 = 0-1 = -1, so a(1) = 1.
b(5-1)-5 = 2-5 = -3, so a(3) = 5.

Prog

(Python)
def a(n):
    a = [0]
    for i in range(1, n):
        a+=[-1]
    countA = 1
    seq = [0]
    m = 1
    while(countA < n):
        x = seq[m-1]-m
        if(x<0):
            if(-x < n and a[-x]==-1):
                a[-x] = m
                countA+=1
            seq+=[seq[m-1]+m]
        else:
            if(x not in seq):
                seq+=[x]
            else:
                seq+=[seq[m-1]+m]
        m+=1
    return a #find all terms in range(0, n)

Crossrefs

Cf. A005132, A057167.

Sequence in context: A209828 A133541 A145536 * A249959 A250013 A258842

Adjacent sequences: A375115 A375116 A375117 * A375119 A375121 A375122

Keyword

nonn

Author

Jens Askgaard, Jul 30 2024

Status

approved