A258073 -id:A258073 - cp's OEIS frontend

A258091 Smallest prime factor of 1+78557*2^n, cf. A258073.

5, 3, 73, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 19, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 37, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 71, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 19, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 37, 3, 5, 3, 7, 3, 5, 3, 13, 3, 5, 3, 73, 3, 5, 3, 7, 3, 5, 3

Offset: 1

Reinhard Zumkeller, May 19 2015

a(n) = A020639(A258073(a(n)));
a(n) <= 73; see also A258095.
Periodic, a(n) = a(n + 840420) for all n (and 840420 is minimal with this property). The only values that occur, are {3, 5, 7, 13, 19, 37, 73} union {47, 59, 71}. - Jeppe Stig Nielsen, Jul 19 2020

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Sierpinski Number

Cf. A020639, A258073, A258095.

Haskell
```
a258091 = a020639 . a258073
```

a(n)=forprime(p=2,,78557*Mod(2,p)^n+1==0 && return(p)) \\ Jeppe Stig Nielsen, Jul 19 2020

A258095 Numbers m, such that the smallest prime factor of 1+78557*2^m doesn't belong to the covering set {3, 5, 7, 13, 19, 37, 73}.

Original entry on oeis.org

39, 183, 219, 1047, 1227, 1299, 1875, 2271, 2559, 2703, 3315, 3531, 3819, 4359, 5079, 5187, 5403, 6015, 6339, 6447, 6843, 7491, 7599, 7671, 8499, 8535, 8859, 9327, 9579, 10119, 10155, 10623, 10983, 11379, 11667, 11811, 12639, 12711, 13467, 13755, 13899

Offset: 1

Reinhard Zumkeller, May 19 2015

nonn

A258091(a(n)) < 73, as each term in A258073 has at least one prime factor in the covering set.

			a(1) = 39; A258073(39) = 43187167471599617 = 71 * 73 * 211 * 39490356709, and 71 is not an element of the covering set.

Reinhard Zumkeller, Table of n, a(n) for n = 1..250
Wikipedia, Sierpinski Number
Wikipedia, Covering set

Cf. A258073, A258091, A020639.

a258095 n = a258095_list !! (n-1)
a258095_list = filter
               (\x -> a258091 x `notElem` [3, 5, 7, 13, 19, 37, 73]) [1..]

A279798 Largest prime factor of 78557*2^n + 1.

Original entry on oeis.org

67, 104743, 8609, 281, 521, 1163, 1436471, 12391, 136343, 1483, 23663, 727, 10453, 2029, 135481883, 7429021, 2059324621, 6864415403, 3716857, 9629, 451358821, 51782483, 62504399, 439322585771, 63337, 128110399, 42209, 59569669, 111486983, 10936129, 31585821557

Offset: 1

Seiichi Manyama, Dec 19 2016

nonn

a(n) <= A258073(n) / A258091(n).

			78557 * 2^1 + 1 = 157115 = 5 * 7 * 67^2. So a(1) = 67.
78557 * 2^2 + 1 = 314229 = 3 * 104743. So a(2) = 104743.

Daniel Suteu, Table of n, a(n) for n = 1..412
Wikipedia, Sierpinski Number

Cf. A002587, A258073, A258091.

Table[FactorInteger[2^n * 78557 + 1][[-1, 1]], {n, 30}] (* Alonso del Arte, Jan 01 2017 *)

a(n) = my(k=78557*2^n+1); factor(k)[omega(k), 1] \\ Felix Fröhlich, Jan 01 2017

a(n) = A006530(A258073(n)).

cp's OEIS Frontend

A258091 Smallest prime factor of 1+78557*2^n, cf. A258073.

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A258095 Numbers m, such that the smallest prime factor of 1+78557*2^m doesn't belong to the covering set {3, 5, 7, 13, 19, 37, 73}.

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A279798 Largest prime factor of 78557*2^n + 1.

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