A125964 -id:A125964 - cp's OEIS frontend

A156018 Primes of the form k^3 + k^2 + k - 1.

2, 13, 83, 257, 1109, 2953, 6173, 8419, 14423, 40493, 99497, 127549, 178807, 198533, 347969, 378503, 480713, 599843, 787243, 1271483, 1417583, 1574467, 2883593, 3133597, 3397649, 4770023, 5118203, 5482927, 5671613, 6469637, 6680203

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 01 2009

nonn

			13 is a term since 13 = 2^3 + 2^2 + 2 - 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A125964.

lst={};Do[p=(n^1+n^2+n^3)-1;If[PrimeQ[p],AppendTo[lst,p]],{n,7!}];lst

A156021 Numbers k such that k^1 + k^2 + k^3 + k^4 -+ 1 are twin primes.

Original entry on oeis.org

1, 2, 12, 30, 44, 50, 63, 74, 110, 165, 177, 222, 239, 254, 327, 492, 519, 804, 942, 954, 1007, 1343, 1352, 1520, 1770, 2375, 2450, 2658, 2795, 2945, 2994, 3075, 3332, 3527, 3548, 3803, 3915, 3935, 4025, 4653, 4704, 4785, 4808, 4862, 5270, 5310, 5364, 5370

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 01 2009

			2 is a term since 2 + 2^2 + 2^3 + 2^4 - 1 = 29 and 2 + 2^2 + 2^3 + 2^4 + 1 = 31 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A125964, A156018.

[n: n in [1..6*10^3] | IsPrime(n^4+n^3+n^2+n-1) and IsPrime(n^4+n^3+n^2+n+1)]; // Vincenzo Librandi, Dec 26 2015

lst={};Do[p=(n^1+n^2+n^3+n^4);If[PrimeQ[p-1]&&PrimeQ[p+1],AppendTo[lst,n]],{n,8!}];lst

A156026 Lesser of twin primes of the form k^1 + k^2 + k^3 + k^4 - 1.

Original entry on oeis.org

3, 29, 22619, 837929, 3835259, 6377549, 16007039, 30397349, 147753209, 745720139, 987082979, 2439903209, 3276517919, 4178766089, 11468884079, 58714318139, 72695416559, 418374010739, 788251653689, 829180295189

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 01 2009

nonn

The corresponding values of k are 1, 2, 12, 30, 44, ... (A156021).

			29 is a term since 2 + 2^2 + 2^3 + 2^4 - 1 = 29 and 2 + 2^2 + 2^3 + 2^4 + 1 = 31 are twin primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001359, A125964, A156018, A156021.

lst={};Do[p=(n^1+n^2+n^3+n^4);If[PrimeQ[p1=p-1]&&PrimeQ[p2=p+1],AppendTo[lst,p1]],{n,8!}];lst
Select[Table[n+n^2+n^3+n^4-1,{n,1000}],AllTrue[{#,#+2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 17 2019 *)

A156027 Greater of twin primes pairs of the form k^1 + k^2 + k^3 + k^4 - 1.

Original entry on oeis.org

5, 31, 22621, 837931, 3835261, 6377551, 16007041, 30397351, 147753211, 745720141, 987082981, 2439903211, 3276517921, 4178766091, 11468884081, 58714318141, 72695416561, 418374010741, 788251653691, 829180295191, 1029317536801, 3255573820801, 3343706188681

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 01 2009

nonn

The corresponding values of k: 1, 2, 12, 30, 44, 50, 63, 74, 110, 165, 177, 222, 239, 254, 327, 492, 519, 804, 942, 954,...

			2 + 2^2 + 2^3 + 2^4 - 1 = 29 and 2 + 2^2 + 2^3 + 2^4 + 1 = 31.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A125964, A156018, A156021, A156026.

[p+2:k in [1..1500] | IsPrime(p) and IsPrime(p+2) where p is k^1+k^2+k^3+k^4-1]; // Marius A. Burtea, Dec 21 2019

lst={};Do[p=(n^1+n^2+n^3+n^4);If[PrimeQ[p1=p-1]&&PrimeQ[p2=p+1],AppendTo[lst,p2]],{n,8!}];lst

More terms from Amiram Eldar, Dec 21 2019

A265670 Numbers n such that n^5 + n^4 + n^3 + n^2 + n - 1 is prime.

Original entry on oeis.org

2, 8, 10, 12, 16, 18, 22, 24, 28, 32, 42, 50, 60, 68, 70, 78, 88, 104, 108, 118, 132, 138, 206, 238, 240, 242, 270, 282, 300, 306, 312, 318, 338, 372, 376, 382, 390, 394, 398, 418, 440, 452, 464, 512, 522, 532, 534, 548, 566, 586, 594, 626, 630, 636, 640, 650

Offset: 1

Vincenzo Librandi, Dec 13 2015

All terms are even. - Altug Alkan, Dec 13 2015

			2 is in the sequence because 2^5 + 2^4 + 2^3 + 2^2 + 2 - 1 = 61 is prime.

Cf. A045546, A100331, A125964, A182424.

[n: n in [0..700] | IsPrime(s) where s is n^5+n^4+n^3+n^2+n-1];

Select[Range[700], PrimeQ[Total[#^Range[1, 5, 1]] - 1] &]

print1(2, ", "); forcomposite(n=1, 1e4, if(ispseudoprime(n^5 + n^4 + n^3 + n^2 + n - 1), print1(n, ", "))) \\ Altug Alkan, Dec 13 2015

cp's OEIS Frontend

A156018 Primes of the form k^3 + k^2 + k - 1.

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A156021 Numbers k such that k^1 + k^2 + k^3 + k^4 -+ 1 are twin primes.

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A156026 Lesser of twin primes of the form k^1 + k^2 + k^3 + k^4 - 1.

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A156027 Greater of twin primes pairs of the form k^1 + k^2 + k^3 + k^4 - 1.

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A265670 Numbers n such that n^5 + n^4 + n^3 + n^2 + n - 1 is prime.

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