A130437 -id:A130437 - cp's OEIS frontend

A108162 Least even pseudoprime > p to base p, where p = prime(n).

161038, 286, 124, 16806, 70, 244, 1228, 906, 154, 52, 66, 66, 344, 526974, 506, 286, 946, 130, 154, 370, 276, 2626, 1558, 19126, 176, 190, 946, 742, 186, 176, 3486, 190, 148, 246, 412, 10930, 186, 186, 3818, 14444, 1246, 316, 286, 276, 532, 426, 310, 246

Offset: 1

Alexander Adamchuk, May 26 2007

nonn

Some numbers appear as a multiple terms in a(n). For example, a(n) = 946 for n = {17,27,64,66,73,75,97,113,114,117,128,139,143,152,153,155} for corresponding prime p = {59,103,311,317,367,379,509,617,619,643,719,797,823,881,883,907}. There are some twin terms such that a(n) = a(n+1). For example, a(11) = a(12) = 66, a(37) = a(38) = 186, a(113) = a(114) = 946, a(152) = a(153) = 946, a(227) = a(228) = 2626.

The indices of records are 1, 14, 354, 549, 1302, 2679, 3743, 3998, 4627, 6880, ... with record values of 161038, 526974, 1234806, 1893126, 1930546, 3347398, 3860962, 5073706, 6376126, 61161946, ... - Amiram Eldar, Sep 10 2019

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Fermat Pseudoprime.
Index entries for sequences related to pseudoprimes

Cf. A006935 (Even pseudoprimes (or primes) to base 2: n divides 2^n - 2, n even).

Cf. A130433, A090082, A130434, A090084, A130435, A130436, A130437, A130438, A130439, A130440, A130441, A130442, A130443.

a[n_] := Module[{p = Prime[n]}, k = p+1; If[OddQ[k], k++]; While[GCD[p, k] != 1 || PowerMod[p, k, k] != p, k+=2]; k]; Array[a, 100] (* Amiram Eldar, Sep 10 2019 *)

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

Original entry on oeis.org

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

Eric Chen, May 17 2015

nonn

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, ...

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

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

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}]

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)))

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

cp's OEIS Frontend

A108162 Least even pseudoprime > p to base p, where p = prime(n).

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