Jason Earls - cp's OEIS frontend

A181113 Numbers n such that n^6 + 1091 is semiprime.

84, 210, 252, 364, 546, 756, 786, 980, 1176, 1380, 1386, 1484, 1614, 1620, 1680, 1722, 1770, 2130, 2478, 2520, 2940, 3114, 3174, 3294, 3330, 3374, 3486, 3516, 3900, 4074, 4158, 4296, 4340, 4410, 4524, 4764, 4920, 4956, 5670, 5844, 6006, 6024, 6066, 6258

Offset: 1

Jason Earls, Oct 04 2010

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A066386.

Select[Range[7300],PrimeOmega[#^6+1091]==2&] (* Harvey P. Dale, Jun 12 2012 *)

A181284 Decimal expansion of sqrt(9/121 * 100^m + (112 - 44*m)/121), where m=30.

Original entry on oeis.org

2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 0, 8, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9

Offset: 30

Jason Earls, Oct 12 2010

			272727272727272727272727272727.2727272727272727272727272727089696969...

Clifford A. Pickover, "Zebra Irrationals," The Mathematics of Oz: Mental Gymnastics From Beyond The Edge. Cambridge University Press, 2002. Page 74.

Seiichi Manyama, Table of n, a(n) for n = 30..50000

First@ RealDigits@ With[{m = 30}, N[Sqrt[9/121*100^m + (112 - 44 m)/121], 120]] (* Michael De Vlieger, Mar 25 2016 *)

sqrt(9e60-1208)/11 \\ Charles R Greathouse IV, Apr 26 2012

A181112 Numbers n such that (n^6 + 1091)/4 is prime.

Original entry on oeis.org

525, 1281, 2709, 3759, 4179, 6531, 9849, 10185, 14385, 15771, 18585, 19929, 21315, 22869, 22995, 23121, 32739, 33285, 39249, 39669, 44499, 46431, 48069, 48531, 49329, 49875, 51891, 54411, 59535, 61131, 62055, 64239, 64365, 67431, 68775

Offset: 1

Jason Earls, Oct 04 2010

Cf. A066386.

Select[Range[70000],PrimeQ[(#^6+1091)/4]&] (* Harvey P. Dale, May 26 2018 *)

is(n)=isprime((n^6+1091)/4) \\ Charles R Greathouse IV, Jun 13 2017

A181114 Numbers n > 0 such that n^6 + 1091 and n^6 + 1093 are both prime.

Original entry on oeis.org

62244, 139230, 171990, 1010100, 1029210, 1275456, 1320774, 1353534, 1356810, 1433796, 1722630, 1842750, 2131584, 2300844, 2396940, 2890524, 2915094, 3357354, 3579030, 3625440, 3631446, 4165980, 4392024, 4408950, 4518150

Offset: 1

Jason Earls, Oct 04 2010

nonn

Cf. A001014, A066386.

IsA181114:=func< n | IsPrime(k+1091) and IsPrime(k+1093) where k is n^6 >; [ n: n in [1..5000000] | IsA181114(n) ]; // Klaus Brockhaus, Feb 17 2011

tpQ[n_]:=Module[{x=n^6+1091},PrimeQ[x]&&PrimeQ[x+2]]
Select[Range[5000000],tpQ] (* Harvey P. Dale, Feb 17 2011 *)

A181186 Number of prime factors of (2^n - 1) * n! + 1, counted with multiplicity.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 3, 3, 2, 2, 3, 2, 3, 5, 3, 2, 1, 3, 2, 2, 3, 3, 2, 6, 1, 4, 4, 3, 3, 3, 2, 2, 4, 3, 5, 2, 4, 2, 4, 1, 4, 4, 3, 3, 1, 3, 4, 5, 3, 4, 4, 5, 2, 2, 2, 6, 4, 2, 5, 3, 7, 4, 3, 2, 5, 3, 4, 4, 4, 2, 7, 6, 7, 3, 5, 2, 4, 3, 8, 8, 6, 4

Offset: 1

Jason Earls, Oct 09 2010

nonn

a(101) >= 3. See link to factordb.com. - Hugo Pfoertner, Aug 07 2019

Yurii Ivanov, Table of n, a(n) for n = 1..103 (terms 1..100 from Sean A. Irvine and Hugo Pfoertner, term 101 from Tyler Busby)
Sean A. Irvine, Factorizations of (2^n-1)*n!+1
factordb.com, Status of (2^n-1)*n!+1.

Cf. A001222, A052589.

Table[PrimeOmega[(2^n-1)n!+1],{n,90}] (* The program takes a long time to run. *) (* Harvey P. Dale, Feb 10 2019 *)

a(n) = A001222(A052589(n)+1). - Michel Marcus, Apr 08 2023

More terms from Sean A. Irvine, Sep 15 2012

A181185 Numbers k such that (2^k - 1) * k! + 1 is prime.

Original entry on oeis.org

1, 2, 3, 6, 17, 25, 40, 45, 143, 289, 510, 524, 526, 716, 756, 1008, 1271, 1370, 3677, 7963, 9053

Offset: 1

Jason Earls, Oct 09 2010

The original motivation for this sequence was in an article by J. Earls, Horace S. Uhler and Some Numbers in His Honor, the author of which no longer wishes to make public. - N. J. A. Sloane, Apr 04 2016

is(n)=ispesudoprime((2^n-1)*n!+1) \\ Charles R Greathouse IV, Jun 13 2017

a(20)-a(21) from Tyler Busby, Mar 10 2024

A181139 Numbers k such that R(k)^3 + R(k)^2 + 1 is prime, where R(k) = (10^k-1)/9.

Original entry on oeis.org

1, 2, 3, 9, 41, 99, 1863, 4019, 8925

Offset: 1

Jason Earls, Oct 06 2010

okQ[n_]:=Module[{x=FromDigits[PadRight[{},n,1]]},PrimeQ[x^3+x^2+1]]; Select[Range[5000],okQ] (* Harvey P. Dale, Nov 04 2011 *)

a(9) from Michael S. Branicky, Mar 22 2024

A181138 Least positive integer k such that n^2 + k is a cube.

Original entry on oeis.org

1, 7, 4, 18, 11, 2, 28, 15, 61, 44, 25, 4, 72, 47, 20, 118, 87, 54, 19, 151, 112, 71, 28, 200, 153, 104, 53, 271, 216, 159, 100, 39, 307, 242, 175, 106, 35, 359, 284, 207, 128, 47, 433, 348, 261, 172, 81, 535, 440, 343, 244, 143, 40, 566, 459, 350, 239, 126, 11

Offset: 0

Jason Earls, Oct 06 2010

a(n) = A070923(n) if n is not cube. Zak Seidov, Mar 26 2013

See A229618 for the range of this sequence. A179386 gives the range of b(n) = min{ a(m); m >= n }. The indices of jumps in this sequence are given in A179388 = { n | a(m)>a(n) for all m > n } = { 0, 5, 11, 181, 207, 225, 500, 524, 1586, ... }. - M. F. Hasler, Sep 26 2013

			a(11) = 4 because 11^2 + k is never a cube for k < 4, but 11^2 + 4 = 5^3. - _Bruno Berselli_, Jan 29 2013

Bruno Berselli, Table of n, a(n) for n = 0..1000 (Corrected Jan 19 2019)

Cf. A070923, A077116.

S:=[];
k:=1;
for n in [0..60] do
   while not IsPower(n^2+k,3) do
        k:=k+1;
   end while;
   Append(~S, k);
   k:=1;
end for;
S;  // Bruno Berselli, Jan 29 2013

Table[(1 + Floor[n^(2/3)])^3 - n^2, {n, 100}] (* Zak Seidov, Mar 26 2013 *)

A181138(n)=(sqrtnint(n^2,3)+1)^3-n^2 \\ Charles R Greathouse IV, Mar 26 2013

a(n) << n^(4/3). - Charles R Greathouse IV, Mar 26 2013

Extended to a(0)=1 by M. F. Hasler, Sep 26 2013

A180923 Numbers n such that 111*n + 1 is prime.

Original entry on oeis.org

2, 16, 18, 20, 26, 28, 30, 38, 40, 42, 46, 56, 60, 62, 68, 72, 82, 86, 88, 96, 110, 112, 118, 130, 132, 138, 140, 150, 156, 158, 160, 166, 178, 192, 196, 210, 216, 220, 226, 228, 240, 242, 248, 250, 266, 276, 278, 280, 290, 292, 300, 306, 320, 326, 342, 348, 350

Offset: 1

Jason Earls, Sep 25 2010

Select[Range[400], PrimeQ[111# + 1] &] (* Harvey P. Dale, Jan 04 2011 *)

is(n)=isprime(111*n+1) \\ Charles R Greathouse IV, Jun 13 2017

A180924 Numbers n such that 12321*2^n + 1 is prime.

Original entry on oeis.org

4, 24, 29, 47, 61, 63, 67, 69, 87, 101, 129, 143, 153, 249, 252, 333, 408, 561, 616, 732, 929, 1349, 3467, 6156, 6919, 9244, 14413, 17128, 20059, 20169, 20512, 23479, 24076, 26208, 27189

Offset: 1

Jason Earls, Sep 25 2010

nonn

is(n)=ispseudoprime(12321<Charles R Greathouse IV, Jun 13 2017

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User: Jason Earls

A181113 Numbers n such that n^6 + 1091 is semiprime.

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A181284 Decimal expansion of sqrt(9/121 * 100^m + (112 - 44*m)/121), where m=30.

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A181112 Numbers n such that (n^6 + 1091)/4 is prime.

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A181114 Numbers n > 0 such that n^6 + 1091 and n^6 + 1093 are both prime.

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A181186 Number of prime factors of (2^n - 1) * n! + 1, counted with multiplicity.

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A181185 Numbers k such that (2^k - 1) * k! + 1 is prime.

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A181139 Numbers k such that R(k)^3 + R(k)^2 + 1 is prime, where R(k) = (10^k-1)/9.

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A181138 Least positive integer k such that n^2 + k is a cube.

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Magma

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A180923 Numbers n such that 111*n + 1 is prime.

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