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.
fQ[n_] := PrimeQ[(n + 1)^5 - n^5]; c = k = 0; Do[ While[k < 10^n + 1, If[ fQ@ k, c++]; k++]; Print[{n, c}], {n, 9}] (* Robert G. Wilson v, Jan 31 2013 *)
Table[Count[#[[2]]-#[[1]]&/@Partition[Range[10^n+1]^7,2,1],?PrimeQ],{n,0,6}] (* _Harvey P. Dale, Sep 17 2019 *)
a(n) = {nb = 0; for (i = 1, 10^n, if (isprime((i+1)^7-i^7), nb++);); nb;} \\ Michel Marcus, Sep 18 2013
As the smallest cuban primes equal to the difference of two consecutive cubes p = (x+1)^3 - x^3, is 7 for x = 1, and as floor (10^(1/2)) = 3, a(0) = a(1) = 0 and a(2) = 1.
cnt = 0; nxt = 1; t = {0}; Do[p = 3*k*(k + 1) + 1; If[p > nxt, AppendTo[t, cnt]; nxt = nxt*Sqrt[10]]; If[PrimeQ[p], cnt++], {k, 100000}]; t (* T. D. Noe, Jan 29 2013 *)
b(n)={my(s=0,k=0,t=1); while(t<=n, s+=isprime(t); k++; t += 6*k); s}
a(n)={b(sqrtint(10^n))} \\ Andrew Howroyd, Jan 14 2020
0^3 - 1^3 + 3*2^3 = 23, 23 is a term. -3^3 + 4^3 - 3*0^3 = -4^3 + 5^3 - 3*2^3 = -52^3 + 53^3 - 3*14^3 = 37, 37 is a term.
p1 = Select[Prime[Range[105]], IntegerQ[(# - 1)/3] &];
p2 = Select[Prime[Range[105]], IntegerQ[(# + 1)/3] &];
n1 = Length@p1; n2 = Length@p2;
r1 = (p1 - 1)/3; r2 = (p2 + 1)/3;
t = {};
Do[x = (z^3 + r1[[n]] + 1/4)^(1/2) - 1/2;
If[IntegerQ[x], AppendTo[t, -x^3 + (x + 1)^3 - 3z^3]], {n, 1,
n1}, {z, 0, 270}]
Do[x = (z^3 - r2[[n]] + 1/4)^(1/2) - 1/2;
If[IntegerQ[x], AppendTo[t, x^3 - (x + 1)^3 + 3z^3]], {n, 1,
n2}, {z, 0, 170}]
Union@t
Comments