[seqfan] A178705
israel at math.ubc.ca
israel at math.ubc.ca
Wed Dec 20 05:06:42 CET 2017
A178705 is "Numbers q that are strong pseudoprimes to some base a,
2<=a<=q-2, such that a^d == 1 mod q"
which I interpret as: odd composite numbers q such that there exists a,
2<=a<=q-2, such that a^d == 1 mod q where d = A000265(q-1).
However, the Data seem to be missing quite a few such numbers:
91, 175, 231, 247, 259, 341, 343, 403, 427, 435, 451, 475, 511, 559, 595,
651, 671, 679, 703, 715, 763, 775, 847, 871, 891, 931, 949, 1015, 1027,
1035, 1075, 1099, 1111, 1147, 1159, 1183, 1247, 1267, 1271, 1331, 1339,
1351, 1387, 1431, 1435, 1491, 1495
For example, 91 should be there because 9^45 == 1 (mod 91), and 175 should
be there because 51^87 = 1 mod 175.
Am I misinterpreting the definition? Is there some reasonable way to define
a sequence with the given Data? Or should the missing numbers be inserted?
Cheers,
Robert
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