A156021 -id:A156021 - cp's OEIS frontend

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

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

cp's OEIS Frontend

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

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