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)=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)=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)=2^5+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)=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)=17764 because 2^4+3^4+5^4+7^4+11^4=17764.
a = 4; Table[Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a, {n, 1, 100}]
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 *)