A285784 Possible nonprime residues of k > p# modulo p# for some primorial p# in A002110.

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

Jamie Morken, Table of n, a(n) for n = 1..1000

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

Cf. A002110, A048863.

Sequence in context: A080466 A271630 A038511 * A062649 A206288 A287390

Adjacent sequences: A285781 A285782 A285783 * A285785 A285786 A285787

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