A235867 G-cyclic numbers k such that A060968(k)^A060968(k) <> 1 (mod k) and A235863(k)^A235863(k) <> 1 (mod k).

77, 119, 133, 187, 217, 253, 287, 301, 319, 323, 341, 391, 399, 403, 407, 413, 437, 469, 517, 551, 553, 559, 583, 589, 623, 651, 667, 707, 713, 731, 737, 749, 779, 781, 803, 817, 851, 869, 871, 889, 893, 899, 903, 913, 917, 935, 943, 959, 969, 1001, 1003

Offset

1,1

Comments

For G-cyclic numbers see A235866.

All terms are composite. - Bill McEachen, Jul 16 2021

Links

Bill McEachen, Table of n, a(n) for n = 1..10000

Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, Fermat test with Gaussian base and Gaussian pseudoprimes, arXiv:1401.4708 [math.NT], 2014.

Prog

(PARI) genit(maxx)={arr2=List(); arr=List(); for(ptr=1, maxx, if( gcd(ptr, A060968(ptr))==1, listput(arr, ptr))); for(ptr=2, #arr, n=arr[ptr]; a=A060968(n)^A060968(n); b=A235863(n)^A235863(n); if(a%n!=1&&b%n!=1, listput(arr2, n))); }
A060968(n)={my(f=factor(n)[, 1]); q=n*prod(i=if(n%2, 1, 2), #f, if(f[i]%4==1, 1-1/f[i], 1+1/f[i]))*if(n%4, 1, 2); return(q); } \\taken from that sequence
A235863(n)={my(f=factor(n)); q=lcm(vector(#f~, i, my([p, e]=f[i, ]); if(p==2, 2^max(e-2, min(e, 2)), p^(e-1)*if(p%4==1, p-1, p+1)))); return (q); } \\taken from that sequence
\\ Bill McEachen, Jul 16 2021

Crossrefs

Cf. A235866, A060968, A235863.

Sequence in context: A127335 A193570 A154534 * A274967 A229826 A330103

Adjacent sequences: A235864 A235865 A235866 * A235868 A235869 A235870

Keyword

nonn

Author

José María Grau Ribas, Feb 22 2014

Status

approved