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A335099 Lexicographically earliest sequence of distinct integers greater than 1 such that a(n) mod a(i)^2 >= a(i) for all i < n. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..59.

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 A075427

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

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Last modified May 17 13:24 EDT 2022. Contains 353746 sequences. (Running on oeis4.)