A253233 Smallest even pseudoprime (>2n+1) in base 2n+1.

4, 286, 124, 16806, 28, 70, 244, 742, 1228, 906, 1852, 154, 28, 286, 52, 66, 496, 442, 66, 1834, 344, 526974, 76, 506, 66, 70, 286, 1266, 2296, 946, 130, 5662, 112, 154, 14246, 370, 276, 8614, 2806, 2626, 112, 1558, 276, 2626, 19126, 1446, 322, 658, 176, 742, 190, 946, 5356, 742, 186, 190, 176, 8474, 2806, 2242, 148

Offset

0,1

Comments

For an even base there are no even pseudoprimes.

Conjecture: There are infinitely many even pseudoprimes in every odd base.

Records: 4, 286, 16806, 526974, 815866, 838246, ..., and they occur at indices: 0, 1, 3, 21, 503, 691, ...

Links

Eric Chen, Table of n, a(n) for n = 0..999 (a(0) corrected by Georg Fischer, Jan 20 2019)

Eric Weisstein's World of Mathematics, Fermat pseudoprime

Wikipedia, Fermat pseudoprime

Index entries for sequences related to pseudoprimes

Formula

a(A005097(n-1)) = A108162(n).

Mathematica

f[n_] := Block[{k = 2 * n + 2}, While[PrimeQ[k] || OddQ[k] || PowerMod[2 * n + 1, k - 1, k] != 1, k++ ]; k]; Table[ f[n], {n, 0, 60}]

Prog

(PARI) a(n) = for(k=n+1, 2^24, if(!isprime(2*k) && Mod(2*n+1, 2*k)^(2*k-1) == Mod(1, 2*k), return(2*k)))

Crossrefs

Cf. A005097, A090082, A090083, A090084, A090085, A090086, A090087, A090088, A090089, A108162, A130433, A130434, A130435, A130436, A130437, A130438, A130439, A130440, A139441, A130442, A130443, A007535.

Sequence in context: A113256 A259495 A090088 * A242997 A221135 A110816

Adjacent sequences: A253230 A253231 A253232 * A253234 A253235 A253236

Keyword

nonn

Author

Eric Chen, May 17 2015

Status

approved