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%I #9 Aug 04 2023 10:13:48
%S 2,8,42,112,368,180,1806,936,840,1600,14168,6216,25120,6272,16770,
%T 52668,83720,24240,103840,29440,35910,184140,278334,197912,282150,
%U 313040,266112,337840,1438722,468540,1254016,319808,1486584,2566432,1321376,2003688,7163646,3121328
%N a(n) is the least practical number A005153(k) such that A005153(k+1) - A005153(k) = 2*n, or -1 if no such number exists.
%H Amiram Eldar, <a href="/A364707/b364707.txt">Table of n, a(n) for n = 1..150</a>
%F a(n) = A005153(A364706(n)).
%e a(1) = 2 since A005153(2) = 2 and A005153(3) = 4 = 2 + 2*1.
%e a(2) = 8 since A005153(5) = 8 and A005153(6) = 12 = 8 + 2*2.
%e a(3) = 42 since A005153(16) = 42 and A005153(17) = 48 = 42 + 2*3.
%t f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[n_] := (ind = Position[(fct = FactorInteger[n])[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most @ fct]), _?(# > 1 &)]) == {};
%t seq[len_, nmax_] := Module[{s = Table[0, {len}], n = 2, prev = 2, c = 0, i}, While[c < len && n <= nmax, n+=2; If[pracQ[n], i = (n - prev)/2; If[i <= len && s[[i]] == 0, c++; s[[i]] = prev]; prev= n]]; s]; seq[20, 10^6]
%Y Cf. A005153, A179651, A330870, A364706.
%K nonn
%O 1,1
%A _Amiram Eldar_, Aug 04 2023
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