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A285784
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Possible nonprime residues of k > p# modulo p# for some primorial p# in A002110.
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6
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1, 121, 143, 169, 187, 209, 221, 247, 289, 299, 323, 361, 377, 391, 403, 437, 481, 493, 527, 529, 533, 551, 559, 589, 611, 629, 667, 689, 697, 703, 713, 731, 767, 779, 793, 799, 817, 841, 851, 871, 893, 899, 901, 923, 943, 949, 961, 989, 1003, 1007, 1027, 1037, 1073, 1079, 1081
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OFFSET
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1,2
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COMMENTS
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Original name: Union of nonprimes p_n# < k < p_(n+1)# and gcd(k, p_n#) = 1, with p_n# = A002110(n).
Let p_n# = A002110(n). This sequence includes nonprime p_n# < k < p_(n+1)# but does not repeat terms that have already appeared in the sequence (mainly 1 for p_n# with n > 1).
If regarded as a number triangle T(n,k), row length <= A048863(n). (End)
Relevant for sieving primes with a wheel of circumference p#: For the 2*3*5 wheel, the only relevant nonprime residue is 1, while for a 2*3*5*7 wheel, there are 5 more nonprime residues {121, 143, 169, 187, 209}. - M. F. Hasler, Mar 25 2019
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LINKS
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EXAMPLE
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Primorial(2) = 2*3 = 6 has two totatives (1 and 5), primorial(3) = 2*3*5 = 30 has eight totatives (1,7,11,13,17,19,23,29), etc.
Taking the union of these lists and removing the primes gives the sequence.
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MATHEMATICA
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MapIndexed[Select[Range @@ #1, Function[k, And[If[First@ #2 == 1, ! PrimeQ@ k, CompositeQ@ k > 1], CoprimeQ[Last@ #1, k]]]] &, Partition[FoldList[#1 #2 &, 1, Prime@ Range@ 5], 2, 1]] // Flatten (* Michael De Vlieger, May 24 2017 *)
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PROG
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(PARI) select( n->!isprime(n), setunion((S(p, M)=Set(primes([1, p*M])%M))(11, 210), S(13, 2310))) \\ M. F. Hasler, Mar 25 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Incorrect definition replaced and more terms added by M. F. Hasler, Mar 25 2019
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STATUS
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approved
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