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Beattific 'primes': numbers n > 1 not equal to floor(k*m*phi) or floor(k*m*phi^2) for any smaller element k in this sequence and any positive integer m.
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Beattific 'primes': numbers n > 1 not divisible equal to floor(k*phi) or floor(k*phi^2) for any smaller element k in this sequence.
BPbp[limit_] := (*Find all the Beattific primes up to limit*)
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BP[lim_limit_] := (* Find all the Beattific primes up to lim limit*)
Module[{r = (1 + Sqrt[5])/2, s = r^2, sieve, = ConstantArray[1, limit = lim, n, k, ]},
Do[If[sieve[[n]] == 1,
list}, sieve = [[Table[1, Floor[k n r], {k, (limit + 1)/(n r)}]]] = 0;
For[n = 2, n <= limit, n++,
If[ sieve[[Table[Floor[k n] r r] == , {k, (limit + 1, )/(n r r)}]]] = 0],
For[k = 1, k n r < limit, k++, sieve[[Floor[k n r]]] = 0];
For[k = 1, k n r r < limit, k++, sieve[[Floor[k n r r]]] = 0]]];
list = {};
For[n = 2, n <= limit, n++,
If[sieve[[n]] == 1, list = Append[list, n]]]; Return[list]]
{n, 2, limit}];
Rest@Flatten@Position[sieve, 1]];
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