A045751 -id:A045751 - cp's OEIS frontend

A260821 Least positive integer k for which n*2^(2^k) + 1 is composite.

5, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 3, 1, 2, 3, 1, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 5, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 2

Offset: 1

Marco Ripà, Jul 31 2015

nonn

a(n) = 1 for nonzero n in A045751. - Michel Marcus, Aug 01 2015

			a(7)=3 because 7*2^2 + 1 = 29 is prime and 7*2^(2^2) + 1 = 113 is also prime, while 7*2^(2^3) + 1 = 11*163.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A045751, A005098.

A260821[n_] := Module[{k = 0}, While[PrimeQ[n*2^(2^++k) + 1]]; k];
Array[A260821, 100] (* Paolo Xausa, Jan 31 2024 *)

a(n) = {k = 1; while (isprime(n*2^2^k+1), k++); k;} \\ Michel Marcus, Aug 01 2015

More terms from Michel Marcus, Aug 01 2015

A107615 Coefficient list length of Poincaré-like polynomials made from A047845, indices of 4*n+1 nonprimes as the m(i) exponents.

Original entry on oeis.org

1, 2, 7, 18, 31, 48, 71, 96, 125, 158, 193, 232, 273, 316, 363, 416, 475, 536, 599, 664, 731, 802, 875, 952, 1033, 1116, 1201, 1290, 1383, 1478, 1579

Offset: 1

Roger L. Bagula, May 16 2007

Cf. A045751.

a = Flatten[Table[If[PrimeQ[4*n + 1] == False, n, {}], {n, 0, 50}]]; Table[Length[CoefficientList[Product[1 + t^(2*a[[n]] + 1), {n, 1, m}], t]], { m, 0, Length[a]}]

P(m) = Product[1 + t^(2*A045751(n) + 1), {n, 1, m}] a(n) = Length[CoefficientList[P(n),x]].

A217707 Numbers n such that both 4n-1 and 4n+1 are composite.

Original entry on oeis.org

14, 16, 19, 23, 29, 30, 31, 36, 40, 44, 46, 47, 51, 52, 54, 55, 59, 61, 62, 65, 72, 74, 75, 76, 80, 81, 82, 85, 86, 89, 91, 94, 98, 101, 103, 104, 106, 107, 109, 113, 118, 119, 121, 124, 128, 129, 132, 133, 134, 136, 138, 140, 145, 146, 149, 151, 156, 157, 159

Offset: 1

Jayanta Basu, Mar 20 2013

Cf. A060461, A045751.

Select[Range[200], ! PrimeQ[4 # - 1] && ! PrimeQ[4 # + 1] &]
Select[Range[200],AllTrue[4#+{1,-1},CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 11 2015 *)

cp's OEIS Frontend

A260821 Least positive integer k for which n*2^(2^k) + 1 is composite.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A107615 Coefficient list length of Poincaré-like polynomials made from A047845, indices of 4*n+1 nonprimes as the m(i) exponents.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A217707 Numbers n such that both 4n-1 and 4n+1 are composite.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

cp's OEIS Frontend

A260821 Least positive integer k for which n*2^(2^k) + 1 is composite.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A107615 Coefficient list length of Poincaré-like polynomials made from A047845, indices of 4*n+1 nonprimes as the m(i) exponents.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

A217707 Numbers n such that both 4*n-1 and 4*n+1 are composite.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A217707 Numbers n such that both 4n-1 and 4n+1 are composite.