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A001262
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Strong pseudoprimes to base 2.
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35
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2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799, 49141, 52633, 65281, 74665, 80581, 85489, 88357, 90751, 104653, 130561, 196093, 220729, 233017, 252601, 253241, 256999, 271951, 280601, 314821, 357761, 390937, 458989, 476971, 486737
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. K. Guy, Unsolved Problems Theory Numbers, A12.
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 95.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000 (using data from A001567)
Joerg Arndt, Fxtbook, section 39.10, pp.786-792
Eric Weisstein's World of Mathematics, Pseudoprime
Eric Weisstein's World of Mathematics, Strong Pseudoprime
Index entries for sequences related to pseudoprimes
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MAPLE
| A007814 := proc(n) padic[ordp](n, 2) ; end proc:
isStrongPsp := proc(n, b) local d, s, r; if type(n, 'even') or n<=1 then return false; elif isprime(n) then return false; else s := A007814(n-1) ; d := (n-1)/2^s ; if modp(b &^ d, n) = 1 then return true; else for r from 0 to s-1 do if modp(b &^ d, n) = n-1 then return true; end if; d := 2*d ; end do: return false; end if; end if; end proc:
isA001262 := proc(n) isStrongPsp(n, 2) ; end proc:
for n from 1 by 2 do if isA001262(n) then print(n); end if; end do: # R. J. Mathar, Apr 05 2011
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MATHEMATICA
| sppQ[n_?EvenQ, _] := False; sppQ[n_?PrimeQ, _] := False; sppQ[n_, b_] := (s = IntegerExponent[n-1, 2]; d = (n-1)/2^s; If[PowerMod[b, d, n] == 1, Return[True], Do[If[PowerMod[b, d, n] == n-1, Return[True]]; d = 2*d, {s}]]); A001262 = {}; n = 1; While[n < 500000, n = n+2; If[sppQ[n, 2] == True, Print[n]; AppendTo[A001262, n]]]; A001262 (* From Jean-François Alcover, Oct 20 2011, after R. J. Mathar *)
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CROSSREFS
| Cf. A001567 (pseudoprimes to base 2), A020229 (Strong Psp base 3).
Sequence in context: A024021 A145590 A038462 * A141232 A062568 A180065
Adjacent sequences: A001259 A001260 A001261 * A001263 A001264 A001265
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson Aug 15 1996.
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