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A335099
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Lexicographically earliest sequence of distinct integers greater than 1 such that a(n) mod a(i)^2 >= a(i) for all i < n.
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0
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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
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..59.
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PROG
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(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
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CROSSREFS
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Cf. A000960, A000040.
Sequence in context: A256800 A172105 A092482 * A147303 A346593 A075427
Adjacent sequences: A335096 A335097 A335098 * A335100 A335101 A335102
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KEYWORD
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nonn,easy
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AUTHOR
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James Kilfiger, Sep 12 2020 (suggested by student)
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EXTENSIONS
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Terms a(29) and beyond from Andrew Howroyd, Sep 12 2020
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STATUS
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approved
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