A020136 -id:A020136 - cp's OEIS frontend

A247307 Numbers of the form (4^k - 4)/k.

0, 6, 20, 63, 204, 682, 2340, 381300, 1398101, 5162220, 71582788, 1010580540, 14467258260, 3059510616420, 2573485501354569, 9938978487990060, 148764065110560900, 510526106256177860940, 117943982401427236556700, 1799331452449680632120820

Offset: 1

Juri-Stepan Gerasimov, Sep 11 2014

nonn

Subsequence of A246445.
Generated by k = 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 15, 17, 19, 23, 28, 29, 31,. ..
This set of k contains all terms of A122781 and all primes. [It contains the primes because j^p == j (mod p) for every integer j if p is prime; see e.g. the corollary 4.4 to the Lagrange theorem in Jones et al.]

			a(9) = 1398101 because (4^12 - 4)/12 = 1398101 for k = 12.

G. A. Jones and J. M. Jones, Congruences with a prime-power modulus, p 65-82 in "Elementary Number Theory", Springer Undergraduate Mathematics Series, (1988).

Cf. A020136, A064535, A122781, A246445, A247033.

lista(nn) = {for (k=1, nn, va = (4^k - 4)/k; if (type(va) == "t_INT", print1(va, ", ")););} \\ Michel Marcus, Sep 12 2014

A243292 Odd numbers n such that (4^n - 1)/3 is a base-2 pseudoprime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Arkadiusz Wesolowski, Jun 02 2014

nonn

Odd numbers not divisible by 3 that are primes or pseudoprimes to base 4.

Wikipedia, Fermat pseudoprime
Index entries for sequences related to pseudoprimes

Cf. A000040, A001567, A020136, A210454.

[n: n in [1..271 by 2] | not n mod 3 eq 0 and IsOne(4^(n-1) mod n)];

A247906 a(n) = n-th pseudoprime to base n.

Original entry on oeis.org

561, 286, 341, 781, 1105, 1105, 133, 364, 703, 793, 1105, 1099, 1891, 6541, 1271, 3991, 1649, 1849, 3059, 7363, 2047, 1738, 4537, 1128, 3145, 2993, 5365, 4069, 4097, 7421, 2465, 11305, 2937, 16589, 4495, 2044, 6601, 26885, 13073, 6892, 22945, 3885, 8695, 10879

Offset: 2

Felix Fröhlich, Sep 26 2014

nonn

			a(2) = A001567(2) = 561.
a(3) = A005935(3) = 286.

Cf. A007535, A098650.

Cf. Pseudoprimes to base b: A001567 (b=2), A005935 (b=3), A020136 (b=4), A005936 (b=5), A005937 (b=6), A005938 (b=7), A020137 (b=8), A020138 (b=9).

for(n=2, 20, i=0; forcomposite(c=2, 1e9, if(Mod(n, c)^(c-1)==1, i++; if(i==n, print1(c, ", "); i=0; break({1}))); if(c==1e9, print1(">1e9, "))))

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A247307 Numbers of the form (4^k - 4)/k.

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A243292 Odd numbers n such that (4^n - 1)/3 is a base-2 pseudoprime.

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A247906 a(n) = n-th pseudoprime to base n.

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