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.
333 is a term since 20*333 + 1 = 6661, 80*333 + 1 = 26641, 100*333 + 1 = 33301, and 200*333 + 1 = 66601 are all primes.
q[n_] := AllTrue[{20, 80, 100, 200}, PrimeQ[# * n + 1] &]; Select[Range[40000], q]
is(n) = isprime(20*n + 1) && isprime(80*n + 1) && isprime(100*n + 1) && isprime(200*n + 1);
95 is a term since 72*95 + 1 = 6841, 576*95 + 1 = 54721, 648*95 + 1 = 61561, 1296*95 + 1 = 123121, and 2592*95 + 1 = 246241 are all primes.
q[n_] := AllTrue[{72, 576, 648, 1296, 2592}, PrimeQ[#*n + 1] &]; Select[Range[200000], q]
is(n) = isprime(72*n + 1) && isprime(576*n + 1) && isprime(648*n + 1) && isprime(1296*n + 1) && isprime(2592*n + 1);
a(1) = 2, because 9*1*2 + 1 = 19 is prime and no lesser number has this property.
p[m_, n_] := AllTrue[Range[n], PrimeQ[9*#*m + 1] &];
a[n_] := a[n] = Module[{m = 1}, While[! p[m, n], m++]; m]
Table[a[n], {n, 1, 9}] (* Robert P. P. McKone, May 02 2024 *)
is(n,m)=my(u=vector(n,k,9*k*m+1));for(i=1,n,if(!isprime(u[i]),return(0)));1 a(n)=my(pas=1);if(n<15,if(n>2,pas=factorback(primes(primepi(n)));pas/=3;my(m=pas));forstep(m=pas,+oo,pas,if(is(n,m),return(m))))
See PARI link
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