A229855 -id:A229855

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A229856

Primes of the form 384*n + 257.

+10
4

257, 641, 1409, 3329, 4481, 7937, 9473, 9857, 11393, 11777, 12161, 13313, 13697, 14081, 15233, 16001, 17921, 19073, 19457, 19841, 21377, 23297, 25601, 28289, 30593, 30977, 35201, 35969, 36353, 37889, 38273, 39041, 40193, 40577, 40961, 41729, 43649, 44417

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Every Fermat number greater than 257 has a prime factor of the form 384*n + 257, n > 0.

LINKS

Table of n, a(n) for n=1..38.

Wikipedia, Fermat number

MATHEMATICA

Select[Table[384*n + 257, {n, 0, 115}], PrimeQ]

PROG

(Magma) [384*n+257 : n in [0..115] | IsPrime(384*n+257)]

CROSSREFS

Subsequence of A107181 (primes of the form 8x^2+9y^2).

Cf. A000215, A023394, A094358, A229853, A229855, A229856.

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Oct 01 2013

STATUS

approved

A229854

Primes of the form 384*n + 1.

+10
3

769, 1153, 2689, 3457, 4993, 6529, 7297, 7681, 9601, 10369, 10753, 12289, 13441, 14593, 15361, 18049, 18433, 20353, 21121, 22273, 23041, 26113, 26497, 26881, 29569, 31489, 31873, 32257, 33409, 36097, 37633, 39937, 43777, 45697, 49537, 49921, 52609, 53377

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Not every composite Fermat number has a prime factor of the form 384*n + 1.

LINKS

Table of n, a(n) for n=1..38.

Wikipedia, Fermat number

MATHEMATICA

Select[Table[384*n + 1, {n, 139}], PrimeQ]

PROG

(Magma) [384*n+1 : n in [1..139] | IsPrime(384*n+1)]

CROSSREFS

Subsequence of A002476 (primes of form 6m + 1).

Cf. A000215, A023394, A094358, A229850, A229853, A229855, A229856.

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Oct 01 2013

STATUS

approved

A242215

a(n) = 18*n + 5.

+10
2

5, 23, 41, 59, 77, 95, 113, 131, 149, 167, 185, 203, 221, 239, 257, 275, 293, 311, 329, 347, 365, 383, 401, 419, 437, 455, 473, 491, 509, 527, 545, 563, 581, 599, 617, 635, 653, 671, 689, 707, 725, 743, 761, 779, 797, 815, 833, 851, 869, 887, 905, 923, 941, 959

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Conjecture: there are infinitely many composite Fermat numbers such that no one of them has a divisor that belongs to this sequence.

LINKS

Table of n, a(n) for n=0..53.

Wikipedia, Fermat number

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

G.f.: (5 + 13*x)/(1 - x)^2.

MAPLE

seq(18*n+5, n=0..53);

MATHEMATICA

Table[18*n + 5, {n, 0, 53}]

LinearRecurrence[{2, -1}, {5, 23}, 60] (* Harvey P. Dale, Aug 25 2017 *)

PROG

(Magma) [18*n+5: n in [0..53]];

(PARI) for(n=0, 53, print1(18*n+5, ", "));

CROSSREFS

Supersequence of A061240. Cf. A229855.

KEYWORD

nonn,easy

AUTHOR

Arkadiusz Wesolowski, May 07 2014

STATUS

approved

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