login
A285784
Possible nonprime residues of k > p# modulo p# for some primorial p# in A002110.
7
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
OFFSET
1,2
COMMENTS
Original name: Union of nonprimes p_n# < k < p_(n+1)# and gcd(k, p_n#) = 1, with p_n# = A002110(n).
From Michael De Vlieger, May 24 2017: (Start)
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
LINKS
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A080466 A271630 A038511 * A062649 A206288 A287390
KEYWORD
nonn
AUTHOR
Jamie Morken, Apr 26 2017
EXTENSIONS
Edited by N. J. A. Sloane, May 01 2017
Incorrect definition replaced and more terms added by M. F. Hasler, Mar 25 2019
STATUS
approved