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A267288 Composites c where at least one base b with 1 < b < c exists such that b^(c-1) == 1 (mod c^2), i.e., composites c that are base-b 'Wieferich pseudoprimes' for at least one b between 1 and c. 4

%I #13 Jan 13 2016 00:12:37

%S 133,451,561,871,904,1065,1105,1267,1729,1891,2059,2201,2501,2821,

%T 2993,3145,4641,5005,5551,5841,5963,6409,6541,6601,6697,7107,7471,

%U 7501,8321,8323,9637,10585,11266,12209,12403,13571,13585,16471,17261,17466,17770,18103

%N Composites c where at least one base b with 1 < b < c exists such that b^(c-1) == 1 (mod c^2), i.e., composites c that are base-b 'Wieferich pseudoprimes' for at least one b between 1 and c.

%C A002808(i) such that A256517(i) < A002808(i).

%C Any term is also a term of A039769.

%e 871 is a term of the sequence, since 699^870 == 1 (mod 871^2) and 699 < 871.

%o (PARI) forcomposite(c=2, , for(b=2, c-1, if(Mod(b, c^2)^(c-1)==1, print1(c, ", "); break({1}))))

%Y Cf. A039769, A134307, A255885, A256517.

%K nonn

%O 1,1

%A _Felix Fröhlich_, Jan 12 2016

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Last modified June 5 10:42 EDT 2024. Contains 373105 sequences. (Running on oeis4.)