A100812 {a(n)} is monotone increasing, with a(1)=1, a(2)=3 and, for n>2, a(n) is the smallest integer such that a(n) mod a(j) is never a(i) for any pair i,j with 1<=i<j<n.

1, 3, 5, 9, 15, 17, 27, 29, 45, 47, 87, 89, 135, 227, 267, 269, 540, 674, 947, 1217, 1442, 1485, 2522, 2564, 2792, 2832, 2834, 2972, 3102, 3240, 3242, 3645, 3737, 4142, 4182, 4320, 4992, 5400, 5807, 6077, 7017, 7967, 8370, 8772, 8774, 9677, 9717, 9990, 9992

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..1833 (first 200 terms from Francisco J. Muñoz, terms <= 2*10^7)

David A. Corneth, PARI program

Example

a(8)<>28, since 28=1 mod 27. But the residues of 29 modulo 3,5,9,15,17 and 27 are 2,4,2,14,12 and 2, none of which are earlier terms of the sequence, so a(8)=29.

Prog

(R)
monotone_increasing <- function(N) {
  a <- c(1, 3)
  while (length(a) < N) {
    candidate <- a[length(a)] + 1
    repeat {
      valid <- TRUE
      for (i in 1:(length(a) - 1)) {
        for (j in (i+1):length(a)) {
          if (candidate %% a[j] == a[i]) {
            valid <- FALSE
            break
          }
        }
        if (!valid) break
      }
      if (valid) {
        a <- c(a, candidate)
        break
      } else {
        candidate <- candidate + 1
      }
    }
  }
  return(a)
}
# Example:
sequence <- monotone_increasing(100)
print(sequence) # Francisco J. Muñoz, Jul 27 2025
(PARI) \\ See Corneth link

Crossrefs

Sequence in context: A339345 A111249 A190804 * A274432 A380544 A190939

Adjacent sequences: A100809 A100810 A100811 * A100813 A100814 A100815

Keyword

nonn

Author

John W. Layman, Jan 05 2005

Status

approved