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)=160 because 2^3+3^3+5^3=160.
a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
a(1)=503 because 2^3+3^3+5^3+7^3=503.
N:= 50: # for a(1)..a(N) P3:= [0,seq(ithprime(i)^3,i=1..N+3)]: S:= ListTools:-PartialSums(P3): seq(S[i+4]-S[i],i=1..N); # Robert Israel, Jan 01 2024
a = 3; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
Total/@Partition[Prime[Range[40]]^3,4,1] (* Harvey P. Dale, Jan 06 2019 *)
a(1)=134067 because 2^6+3^6+5^6+7^6=134067.
a = 6; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
a(1)=20207 because 2^5+3^5+5^5+7^5=20207.
a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a, {n, 1, 100}]
a(1)=722 because 2^4+3^4+5^4=722.
a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
a(1)=3400 because 2^5+3^5+5^5=3400.
a = 5; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a, {n, 1, 100}]
Total[#^5]&/@Partition[Prime[Range[30]],3,1] (* Harvey P. Dale, May 26 2011 *)
a(1)=2315 because 2^7 + 3^7 = 2315.
[NthPrime(n)^7 + NthPrime(n+1)^7: n in [1..25]]; // Vincenzo Librandi, Aug 23 2018
seq(add(ithprime(n+k)^7,k=0..1),n=1..20); # Muniru A Asiru, Aug 22 2018
e = 7; Table[Prime[n]^e + Prime[n + 1]^e, {n, 1, 100}]
Total/@Partition[Prime[Range[20]]^7,2,1] (* Harvey P. Dale, Oct 16 2014 *)
a(n) = prime(n)^7 + prime(n+1)^7; \\ Michel Marcus, Aug 22 2018
a(1)=35 because 2^3+3^3=35.
a = 3; Table[Prime[n]^a + Prime[n + 1]^a, {n, 1, 100}]
Total[#^3]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 29 2021 *)
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}]