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Search: id:A076974
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| A076974 |
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Increasing sequence where each number is unequal to 2 mod all previous numbers. |
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+0
2
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| 2, 3, 7, 13, 19, 25, 31, 39, 43, 49, 55, 61, 69, 73, 81, 85, 91, 99, 103, 109, 115, 123, 129, 133, 139, 147, 151, 159, 165, 169, 175, 181, 187, 193, 199, 207, 213, 225, 229, 235, 241, 253, 259, 265, 271, 279, 283, 291, 295, 309, 313, 319, 333, 337, 349, 355
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Can be generated quickly by modified sieve of Eratosthenes. Note that eliminating numbers that equal zero mod any previous number is exactly the sieve of Eratosthenes and generates the primes; eliminating numbers that equal one mod any previous number just gives the even numbers.
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EXAMPLE
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a(4)=13 because the smaller numbers after a(3)=7 are eliminated: 8=2 (mod 2 or 3), 9=2 (mod 7), 10=2 (mod 2), 11=2 (mod 3), 12=2 (mod 2).
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PROGRAM
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(Python: replace leading dots by blanks before running)
.def A076974():
... D = {}
... q = 2
... while True:
....... if q not in D:
........... yield q
........... D.setdefault(q+2, []).append(q)
....... else:
........... for p in D[q]:
............... D.setdefault(p+q, []).append(p)
........... del D[q]
....... q += 1
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CROSSREFS
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Sequence in context: A130903 A068828 A100764 this_sequence A051484 A101415 A045331
Adjacent sequences: A076971 A076972 A076973 this_sequence A076975 A076976 A076977
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KEYWORD
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easy,nonn
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AUTHOR
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David Eppstein (eppstein(AT)ics.uci.edu), Nov 28 2002
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