A188661 -id:A188661 - cp's OEIS frontend

A188937 Let G be the class group of the imaginary quadratic field Q(sqrt(-A188661(n))); the 2-Sylow subgroup of G is cyclic of order 2^a(n).

2, 3, 3, 4, 5, 6, 8, 9, 6, 10, 7, 6, 9, 8, 10

Offset: 1

N. J. A. Sloane, Apr 14 2011

Daniel Shanks, Gauss's ternary form reduction and the 2-Sylow subgroup, Math. Comp. 25 (1971), 837-853.

A188129 a(n) = (2^n+3)^2-8.

8, 17, 41, 113, 353, 1217, 4481, 17153, 67073, 265217, 1054721, 4206593, 16801793, 67158017, 268533761, 1073938433, 4295360513, 17180655617, 68721049601, 274881052673, 1099517919233, 4398059094017, 17592211210241, 70368794509313, 281475077373953, 1125900108169217, 4503600030023681, 18014399314788353, 72057595648540673

Offset: 0

N. J. A. Sloane, Apr 14 2011

Daniel Shanks, Gauss's ternary form reduction and the 2-Sylow subgroup, Math. Comp. 25 (1971), 837-853.
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

For primes see A188661 and A188936.

(2^Range[0,30]+3)^2-8 (* or *) LinearRecurrence[{7,-14,8},{8,17,41},30] (* Harvey P. Dale, Nov 23 2012 *)

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3). G.f.: -(34*x^2-39*x+8)/((x-1)*(2*x-1)*(4*x-1)). [Colin Barker, Nov 11 2012]

A188936 Numbers k such that (2^k + 3)^2 - 8 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 19, 27, 28, 32, 36, 48, 56, 61, 131, 170, 251, 750, 771, 779, 790, 874, 1176, 1728, 2604, 3541, 5394, 6203, 9230, 14666, 15680, 26712, 45840, 46019, 56220

Offset: 1

N. J. A. Sloane, Apr 14 2011

Daniel Shanks, Gauss's ternary form reduction and the 2-Sylow subgroup, Math. Comp. 25 (1971), 837-853.

Cf. A188129, A188661, A188937.

for(n=1,10^6,if(isprime((2^n+3)^2-8),print1(n,", "))); /* Joerg Arndt, Apr 25 2011 */

a(22)-a(30) from Joerg Arndt, Apr 25 2011
a(31)-a(33) from Vincenzo Librandi, May 13 2011
a(36) from Charles R Greathouse IV, Oct 10 2011
a(37)-a(39) from Charles R Greathouse IV, Oct 11 2011
a(34)-a(35) inserted by Michael S. Branicky, Jul 25 2024

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A188937 Let G be the class group of the imaginary quadratic field Q(sqrt(-A188661(n))); the 2-Sylow subgroup of G is cyclic of order 2^a(n).

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A188129 a(n) = (2^n+3)^2-8.

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A188936 Numbers k such that (2^k + 3)^2 - 8 is prime.

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