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A225917
a(n) is the smallest product of distinct prime pair p*q such that both 2^n*p+q and p+2^n+q are prime numbers.
1
15, 15, 15, 15, 15, 55, 15, 15, 39, 133, 35, 177, 51, 57, 39, 259, 65, 51, 329, 39, 141, 51, 1199, 85, 341, 133, 141, 415, 471, 21, 515, 15, 635, 247, 365, 57, 501, 133, 305, 1501, 159, 111, 411, 1135, 291, 505, 51, 913, 515, 411, 471, 849, 1569, 895, 155, 1897
OFFSET
1,1
EXAMPLE
15=3*5, both 2*3+5=11 and 3+2*5=13 are prime numbers, so a(1)=15;
...
when n=6, for any numbers in the form of p*q that are smaller than 55, 2^6*p+q and p+2^6*q are not both prime numbers. 55=5*11, and 2^6*5+11=331 and 5+2^6*11=709 are prime numbers, so a(6)=55.
MATHEMATICA
NextA046388[n_] := Block[{p1 = Prime[Range[2, PrimePi[Max[3, NextPrime[Ceiling@Sqrt[n + 1] - 1]]]]], p2}, p2 = Table[Max[NextPrime[p1[[i]]], NextPrime[Ceiling[(n + 1)/p1[[i]]] - 1]], {i, Length[p1]}]; Min[p1*p2]]; Table[seed=1; While[seed = NextA046388[seed]; fct = FactorInteger[seed]; p1 = fct[[1, 1]]; p2 = fct[[2, 1]]; c1 = 2^i*p1 + p2; c2 = p1 + 2^i*p2; ! ((PrimeQ[c1]) && (PrimeQ[c2]))]; seed, {i, 1, 56}]
nn = 2000; pq = Select[Range[nn], PrimeOmega[#] == 2 &]; p = Table[FactorInteger[r][[1, 1]], {r, pq}]; q = pq/p; t = {}; n = 1; While[i = 1; While[i <= Length[pq] && ! (PrimeQ[2^n*p[[i]] + q[[i]]] && PrimeQ[2^n*q[[i]] + p[[i]]]), i++]; i <= Length[pq], AppendTo[t, pq[[i]]]; n++]; t (* T. D. Noe, May 21 2013 *)
CROSSREFS
Cf. A225916.
Sequence in context: A010854 A003884 A346623 * A140806 A099610 A085321
KEYWORD
nonn
AUTHOR
Lei Zhou, May 20 2013
STATUS
approved