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 A182221 Composite numbers in A182140 but not in A071700. 1
 255, 385, 34561, 65535, 147455, 195841, 1034881, 4070401, 4746241, 5040001, 16675201, 22704001, 36067201, 47013121, 83623935, 136967041, 168720001, 271878145, 549141119, 613092481, 836567041, 1039779841, 1049759999, 1548072961, 2556902401, 2646067201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A182140 includes the prime numbers and A071700. LINKS J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, Fermat test with gaussian base and Gaussian pseudoprimes, arXiv preprint arXiv:1401.4708 [math.NT], 2014. MATHEMATICA fa=FactorInteger; isA071700[n_]:=Length@fa[n]==2&&fa[n][[1, 2]]==fa[n][[2, 2]]==1&&Mod[Sqrt[n+1], 4]==0; A060968[p_, s_] := Which[Mod[p, 4] == 1, p^(s-1)*(p-1), Mod[p, 4]==3, p^(s-1)*(p+1), s==1, 2, True, 2^(s+1)]; A060968[1]=1; A060968[n_] := Product[A060968[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}]; A201629[n_]:=Which[Mod[n, 4]==1, (n-1), Mod[n, 4]==3, (n+1), True, n]; Select[Range[10000], !isA071700[#]&&!PrimeQ[#]&&A060968[#]==A201629[#]&] PROG (PARI) isA071700(n)=my(k=sqrtint(n\16)); n==16*k^2+32*k+15 && isprime(4*k+3) && isprime(4*k+5) is(n)=if(isprime(n), return(0)); my(f=factor(n)[, 1]); 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)==if(n%2, (n+1)\4*4, n) && !isA071700(n) \\ Charles R Greathouse IV, Jul 03 2013 CROSSREFS Cf. A182140, A071700, A060968, A201629. Sequence in context: A306223 A023690 A101745 * A053339 A031197 A043348 Adjacent sequences:  A182218 A182219 A182220 * A182222 A182223 A182224 KEYWORD nonn AUTHOR José María Grau Ribas, Apr 19 2012 EXTENSIONS a(15)-a(23) from Charles R Greathouse IV, Jul 03 2013 a(24)-a(26) from Charles R Greathouse IV, Jul 05 2013 STATUS approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)