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A020280 Strong pseudoprimes to base 54. 1
55, 341, 361, 385, 1247, 2701, 2863, 4033, 4069, 7957, 9073, 14905, 15409, 21349, 22495, 27157, 29341, 32689, 33227, 37921, 42001, 42121, 42127, 49141, 55831, 56449, 60701, 62893, 70801, 77293, 83333, 107929, 128143, 132193, 145921, 150553, 152497 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Strong Pseudoprime
MATHEMATICA
strongPseudoprimeQ[b_, n_] := Module[{rems = Table[PowerMod[b, (n - 1)/2^expo, n], {expo, 0, IntegerExponent[n - 1, 2]}]}, (rems[[-1]] == 1 || MemberQ[rems, n - 1]) && PowerMod[b, n - 1, n] == 1]; max = 5000; Select[Complement[Range[2, max], Prime[Range[PrimePi[max]]]], strongPseudoprimeQ[54, #] &] (* Alonso del Arte, Aug 03 2018 *)
PROG
(PARI)
oddpart(n) = if (n % 2, n, oddpart(n/2))
isA020280(n) = {local(d, s, res); d = oddpart(n - 1); s = bigomega((n - 1)/d); /* count factors of 2 */
res = 0; if(s != 0 & !isprime(n), /* n is odd and composite */
if (Mod(54, n)^d == Mod(1, n), res = 1, /* 54^d = 1 (mod n) */
for (r = 0, s - 1, if (Mod(54, n)^(d * 2^r) == Mod(-1, n), res = 1)))); res} // 54^(d * 2^r) = -1 (mod n) \\ Michael B. Porter, Oct 23 2009
CROSSREFS
Sequence in context: A140197 A250841 A250834 * A063653 A222348 A075740
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 09:14 EDT 2024. Contains 371268 sequences. (Running on oeis4.)