A293048 Primes of the form 2^q * 3^r * 11^s + 1.
2, 3, 5, 7, 13, 17, 19, 23, 37, 67, 73, 89, 97, 109, 163, 193, 199, 257, 353, 397, 433, 487, 577, 727, 769, 1153, 1297, 1409, 1453, 1459, 1783, 2113, 2179, 2377, 2593, 2663, 2917, 3169, 3457, 3889, 4357, 5347, 6337, 7129, 8713, 10369, 11617, 12289, 15973, 17497, 18433, 19009, 19603
Offset: 1
Keywords
Examples
2 = a(1) = 2^0 * 3^0 * 11^0 + 1. 13 = a(5) = 2^2 * 3^1 * 11^0 + 1 = 13. list of (q, r, s): (0, 0, 0), (1, 0, 0), (2, 0, 0), (1, 1, 0), (2, 1, 0), (4, 0, 0), (1, 2, 0), (2, 0, 1), (2, 2, 0), (1, 1, 1), ...
Crossrefs
Programs
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GAP
K:=10^5+1;; # to get all terms <= K. A:=Filtered([1..K],IsPrime);; I:=[3,11];; B:=List(A,i->Elements(Factors(i-1)));; C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));; A293048:=Concatenation([2],List(Set(Flat(List([1..Length(C)],i->List([1..Length(C[i])],j->Positions(B,C[i][j]))))),i->A[i]));
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Mathematica
With[{n = 20000}, Union@ Select[Flatten@ Table[2^p1*3^p2*11^p5 + 1, {p1, 0, Log[2, n/(1)]}, {p2, 0, Log[3, n/(2^p1)]}, {p5, 0, Log[11, n/(2^p1*3^p2)]}], PrimeQ]] (* Michael De Vlieger, Sep 30 2017 *)
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