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 A238264 Smallest number that can be written in the form 2^k1 * p1^k2 + 2^k3 * p2^k4 in exactly n distinct ways, where p1 and p2 are odd prime numbers and k1,k2,k3,k4 are nonnegative integers. 3

%I

%S 2,4,6,8,10,12,14,18,20,24,26,28,30,36,42,45,48,50,56,54,60,80,72,81,

%T 93,84,115,90,110,105,114,108,129,120,132,144,153,205,150,165,186,168,

%U 189,195,204,180,231,216,234,246,210,279,276,255,240,252,288,270

%N Smallest number that can be written in the form 2^k1 * p1^k2 + 2^k3 * p2^k4 in exactly n distinct ways, where p1 and p2 are odd prime numbers and k1,k2,k3,k4 are nonnegative integers.

%C a(n) is the smallest index k of A238263(k) for all k-s such that A238263(k)=n.

%H Lei Zhou, <a href="/A238264/b238264.txt">Table of n, a(n) for n = 1..10000</a>

%e A238263(2)=A238263(3)=1, Min[2,3]=2, so a(1)=2.

%e ...

%e A238263(50)=A238263(51)=...=A238263[71]=18, Min[50, 51,...,71]=50, so a(18)=50.

%t n = 1; found = 0; s = {}; target = 58; Do[AppendTo[s, 0], {i, 1, target}]; While[found < target, n++; ct = 0; Do[If[f1 = FactorInteger[i]; l1 = Length[f1]; If[f1[[1, 1]] == 2, l1--]; f2 = FactorInteger[n - i]; l2 = Length[f2]; If[f2[[1, 1]] == 2, l2--]; (l1 <= 1) && (l2 <= 1), ct++], {i, 1, Floor[n/2]}]; If[ct <= target, If[s[[ct]] == 0, s[[ct]] = n; found++]]]; s

%Y Cf. A238263, A000961.

%K nonn

%O 1,1

%A _Lei Zhou_, Feb 21 2014

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Last modified August 5 15:07 EDT 2021. Contains 346470 sequences. (Running on oeis4.)