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.
Kellen Shenton has authored 3 sequences.
For p = 17: the product of the primes from 2 to p*2 is 2*3*5*7*11*13*17*19*23*29*31 = 200560490130, and the product of the primes from 2 to p is 2*3*5*7*11*13*17 = 510510. 200560490130 - 510510 + 1 = 200559979621, a prime number.
a(3) = 102795 because: for k = 1; 102795^1-2 = 102793 and 102795^1+2 = 102797, both of which are prime, and for k = 2; 102795^2-2 = 10566812023 and 102795^2+2 = 10566812027, both of which are prime, and for k = 3; 102795^3-2 = 1086215442109873 and 102795^3+2 = 1086215442109877, both of which are prime, and 102795 is the smallest number with this property.
isok(m,n) = for (k=1, n, if(!isprime(m^k-2) || !isprime(m^k+2), return(0));); return(1); a(n) = my(m=1); while(!isok(m, n), m++); m; \\ Michel Marcus, Nov 14 2022
a(6)=448 because 448 is the smallest number b such that 1 + Sum_{k=0..6} b^(2^k) is prime.
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