This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1)=2^4+3^4=97.
a = 4; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
a(1)=2^5+3^5=275.
a = 5; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
a(1)=793 because 2^6+3^6=793.
a = 6; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
a(1)=16418 because 2^6+3^6+5^6=16418.
L:= [seq(ithprime(i)^6,i=1..100)]: L[1..-3]+L[2..-2]+L[3..-1]; # Robert Israel, Jun 28 2018
a = 6; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total/@(Partition[Prime[Range[25]],3,1]^6) (* Harvey P. Dale, Mar 29 2011 *)
a(1)=1834 because 2^3+3^3+5^3+7^3+11^3=1834.
a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total[#^3]&/@Partition[Prime[Range[40]],5,1] (* Harvey P. Dale, May 01 2013 *)
a(1)=20391154 because 2^7+3^7+5^7+7^7+11^7=20391154
a = 7; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[20]]^7,5,1] (* Harvey P. Dale, Mar 05 2022 *)
a(1)=181258 because 2^5+3^5+5^5+7^5+11^5=181258.
a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[30]]^5,5,1] (* Harvey P. Dale, Dec 02 2017 *)
a(1)=1905628 because 2^6+3^6+5^6+7^6+11^6=1905628.
a = 6; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
Total/@(Partition[Prime[Range[30]],5,1]^6) (* Harvey P. Dale, Mar 13 2011 *)
a(1)=208 because 2^2+3^2+5^2+7^2+11^2=208
a = 2; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
87 is a term as 87 = 2^2 + 3^2 + 5^2 + 7^2.
Select[Range@1000,
Length[PowersRepresentations[#, 4, 2] // Select[AllTrue@PrimeQ] //
Select[DuplicateFreeQ]] > 0 &]
upto(n) = {if(n <= 86, return([])); my(pr = primes(primepi(sqrtint(n - 38))), res = List()); forvec(v = vector(4, i, [1, #pr]), c = sum(i = 1, #v, pr[v[i]]^2); if(c <= n, listput(res, c)), 2); listsort(res, 1); res} \\ David A. Corneth, Jul 12 2023
from itertools import combinations as comb ps=[p**2 for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]] a=[n for n in range(1001) if n in [sum(n) for n in list(comb(ps,4))]] print(a)