A239874 -id:A239874 - cp's OEIS frontend

A239925 Integers n such that 2n^2+1, 2n^3+1, 2n^4+1 and 2n^5+1 are prime.

1, 30, 8025, 44250, 49335, 49599, 155061, 218196, 255975, 293754, 324684, 333405, 336045, 367839, 381804, 416796, 476814, 514005, 529650, 558291, 668856, 682716, 747810, 893190, 930336, 933576, 1004004, 1246266, 1270860, 1383126, 1392111, 1427211, 1491645, 1497024, 1745904, 1786551

Offset: 1

Zak Seidov, Mar 29 2014

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..134

Subsequence of A239920. Cf. A089001, A168550, A239874.

Select[Range[0, 2000000], PrimeQ[2 #^2 + 1] && PrimeQ[2 #^3 + 1] && PrimeQ[2 #^4 + 1] && PrimeQ[2 #^5 + 1] &] (* Vincenzo Librandi, Mar 29 2014 *)
Select[Range[179*10^4], AllTrue[2 #^Range[2, 5] + 1, PrimeQ] &] (* Harvey P. Dale, Sep 24 2021 *)

s=[]; for(n=1, 2000000, if(isprime(2*n^2+1) && isprime(2*n^3+1) && isprime(2*n^4+1) && isprime(2*n^5+1), s=concat(s, n))); s \\ Colin Barker, Mar 29 2014

A239920 Integers n such that 2n^2+1, 2n^3+1 and 2n^4+1 are prime.

Original entry on oeis.org

1, 6, 21, 30, 96, 297, 375, 621, 1359, 1704, 1749, 1761, 3696, 3849, 4467, 8025, 8646, 9834, 11352, 15630, 17397, 17949, 19575, 20274, 27087, 28452, 30504, 32154, 32307, 33666, 35670, 36240, 37785, 37962, 39927, 40617, 42987, 44250, 47559, 49335, 49599

Offset: 1

Zak Seidov, Mar 29 2014

nonn

Zak Seidov, Table of n, a(n) for n = 1..1000

Subsequence of A239874. Cf. A089001, A168550.

Select[Range[0, 50000], PrimeQ[2 #^2 + 1] && PrimeQ[2  #^3 + 1] && PrimeQ[2 #^4 + 1]&] (* Vincenzo Librandi, Mar 30 2014 *)

s=[]; for(n=1, 100000, if(isprime(2*n^2+1) && isprime(2*n^3+1) && isprime(2*n^4+1), s=concat(s, n))); s \\ Colin Barker, Mar 29 2014

A240099 Integers n such that 2n^k + 1, for k = 2..6, are prime.

Original entry on oeis.org

1, 44250, 1004004, 3490575, 3517335, 5750115, 10729026, 19193559, 20251770, 25284039, 25552194, 30204801, 33733206, 39015405, 47518809, 52463445, 58370025, 69502971, 72009429, 77086380, 78510156, 83972646, 85955475, 89190969, 90499584, 92246199, 95374005

Offset: 1

Zak Seidov, Apr 01 2014

nonn

Note that 2n^7+1 may or may not be prime.
First n>1 such that 2n^k+1, for k=2..7, are prime, is a(4) = 3490575.
First n>1 such that 2n^k+1, for k=2..8, are prime, is 83972646.
Subsequence of A239925:  a(2) = 44250 = A239925(4),  a(3) = 1004004 = A239925(27).

Cf. A089001, A168550, A239874, A239925.

Select[Range[10^8],AllTrue[2#^Range[2,6]+1,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 18 2015 *)

A240105 Integers m such that 2*m^k + 1, for k = 2..7, are prime.

Original entry on oeis.org

1, 3490575, 83972646, 414180489, 476072025, 1881147720, 3020243916, 3188924769, 3285167214, 3543143220, 6593858205, 8239349955, 10914074124, 14102235060, 15455042889, 16196415300, 16588528539, 16636093485, 17688635511, 17929182270, 18997337436, 19290317670, 19347263739

Offset: 1

Zak Seidov, Apr 01 2014

nonn

First m>1 such that 2*m^k+1, for k=2..8, are prime, is a(3) = 83972646.

Subsequence of A240099: a(2) = 3490575 = A240099(4), a(3) = 83972646 = A240099(22).

Cf. A089001, A168550, A239874, A239925, A240099.

More terms from Jinyuan Wang, Jun 12 2025

cp's OEIS Frontend

A239925 Integers n such that 2n^2+1, 2n^3+1, 2n^4+1 and 2n^5+1 are prime.

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A239920 Integers n such that 2n^2+1, 2n^3+1 and 2n^4+1 are prime.

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A240099 Integers n such that 2n^k + 1, for k = 2..6, are prime.

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A240105 Integers m such that 2*m^k + 1, for k = 2..7, are prime.

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