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A007921
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Numbers that are not the difference of two primes.
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28
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7, 13, 19, 23, 25, 31, 33, 37, 43, 47, 49, 53, 55, 61, 63, 67, 73, 75, 79, 83, 85, 89, 91, 93, 97, 103, 109, 113, 115, 117, 119, 121, 123, 127, 131, 133, 139, 141, 143, 145, 151, 153, 157, 159, 163, 167, 169, 173, 175, 181, 183, 185, 187, 193
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OFFSET
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1,1
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COMMENTS
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Conjecturally, odd numbers k such that k+2 is composite.
It seems that the sequence contains the squares of all primes except 2 and 3. - Ivan N. Ianakiev, Aug 29 2013
Integers d such that A123556(d) = 1, that is, integers d such that the largest possible arithmetic progression (AP) of primes with common difference d has only one element. For each such d, the unique element of all the first largest APs with 1 element is A342309(d) = 2. - Bernard Schott, Jan 08 2023
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REFERENCES
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F. Smarandache, Properties of Numbers, 1972. (See Smarandache odd sieve.)
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LINKS
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Diophante, A1880. NP en PA (prime numbers in arithmetic progression) (in French).
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MAPLE
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filter := d -> irem(d, 2) <> 0 and not isprime(2+d) : select(filter, [`$`(1 .. 200)]); # Bernard Schott, Jan 08 2023
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PROG
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(Haskell)
a007921 n = a007921_list !! (n-1)
a007921_list = filter ((== 0) . a010051' . (+ 2)) [1, 3 ..]
(Python)
from sympy import isprime
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CROSSREFS
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Largest AP of prime numbers with k elements: this sequence (k=1), A359408 (k=2), A206037 (k=3), A359409 (k=4), A206039 (k=5), A359410 (k=6), A206041 (k=7), A206042 (k=8), A206043 (k=9), A206044 (k=10), A206045 (k=11).
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KEYWORD
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nonn,easy,nice
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AUTHOR
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R. Muller
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STATUS
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approved
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