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A235867
G-cyclic numbers k such that A060968(k)^A060968(k) <> 1 (mod k) and A235863(k)^A235863(k) <> 1 (mod k).
1
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved