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%I #12 Feb 23 2018 22:57:54
%S 1,2,3,4,5,6,7,9,8,11,12,13,10,15,14,17,20,21,16,25,18,19,22,27,26,23,
%T 24,29,30,31,28,33,34,37,36,35,32,39,40,41,38,43,46,51,50,47,42,55,48,
%U 49,52,45,44,53,54,59,62,63,58,67,60,61,64,57,56,65,66,71,68,69,70,79,72,77,74,75,76,73,78,85,82
%N a(n) is the smallest positive integer not already in the sequence such that a(n) + a(n-1) is a prime power, with a(1) = 1.
%C Conjectured to be a permutation of the natural numbers.
%H Robert Israel, <a href="/A284049/b284049.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e a(8) = 9 because 1, 2, 3, 4, 5, 6 and 7 have already been used in the sequence, 7 + 8 = 15 is not prime power while 7 + 9 = 16 is a prime power.
%p N:= 100: # to get all terms before the first term > N
%p S:= [$2..N]:
%p a[1]:= 1: found:= true:
%p for n from 2 while found do
%p found:= false;
%p for j from 1 to nops(S) do
%p if ispp(a[n-1]+S[j]) then
%p found:= true;
%p a[n]:= S[j];
%p S:= subsop(j=NULL,S);
%p break
%p fi
%p od;
%p od:
%p seq(a[i],i=1..n-2); # _Robert Israel_, Apr 16 2017
%t f[s_List] := Block[{k = 1, a = s[[-1]]}, While[MemberQ[s, k] || ! PrimePowerQ[a + k], k++]; Append[s, k]]; Nest[f, {1}, 80]
%Y Cf. A000961, A055265, A055266, A121878, A228730, A243625, A246655, A284048.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Mar 19 2017
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