A335099 Lexicographically earliest sequence of distinct integers greater than 1 such that a(n) mod a(i)^2 >= a(i) for all i < n.

2, 3, 6, 7, 14, 15, 22, 23, 26, 30, 31, 34, 35, 42, 43, 58, 59, 62, 66, 67, 70, 71, 78, 79, 86, 87, 94, 95, 106, 107, 114, 115, 122, 123, 130, 131, 134, 138, 139, 142, 143, 158, 159, 166, 167, 170, 174, 175, 178, 179, 186, 187, 194, 195, 210, 211, 214, 215, 222

Offset

1,1

Comments

In the sieve of Eratosthenes, first the even numbers are removed, then the multiples of 3, then multiples of 5. In this sieve first the numbers greater than 2 and modulo 0 or 1 (mod 4) are removed leaving (1) 2, 3, 6, 7, 10, 11, 14, 15. Then the numbers greater than 3 and modulo 0, 1, 2 (mod 9) are removed leaving (1) 2, 3, 6, 7, 14, 15. Then numbers modulo 0, 1, 2, 3, 4, 5 (mod 36) are removed.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 1000: # for terms <= N
R:= NULL:
Cands:= [$2..N]:
while Cands <> [] do
  r:= Cands[1];
  R:= R, r;
  Cands:= select(t -> t mod r^2 >= r, Cands[2..-1]);
od:
R; # Robert Israel, Sep 05 2024

Prog

(Python3)
from math import sqrt
length=100
s=list(range(2, length))
for p in range(int(sqrt(length))):
    x = s[p]
    if x==0 : continue
    for i, e in enumerate(s):
        if e>x and e%(x*x)<x:
            s[i]=0  # mark sieved values as zero
result =[j for j in s if j!=0] # remove zeros
print(result)
(PARI) seq(n)={my(a=vector(n), k=1); for(n=1, #a, while(1, k++; my(f=1); for(i=1, n-1, if(k%a[i]^2<a[i], f=0; break)); if(f, a[n]=k; break))); a} \\ Andrew Howroyd, Sep 12 2020

Crossrefs

Cf. A000960, A000040.

Sequence in context: A256800 A172105 A092482 * A147303 A346593 A066880

Adjacent sequences: A335096 A335097 A335098 * A335100 A335101 A335102

Keyword

nonn,easy

Author

James Kilfiger, Sep 12 2020 (suggested by student)

Extensions

Terms a(29) and beyond from Andrew Howroyd, Sep 12 2020

Status

approved