A284049 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.

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, 24, 29, 30, 31, 28, 33, 34, 37, 36, 35, 32, 39, 40, 41, 38, 43, 46, 51, 50, 47, 42, 55, 48, 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

Offset: 1

Author

Ilya Gutkovskiy, Mar 19 2017

Keywords

• nonn

Comments

Conjectured to be a permutation of the natural numbers.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Power
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000961, A055265, A055266, A121878, A228730, A243625, A246655, A284048.

Programs

Maple

N:= 100: # to get all terms before the first term > N
S:= [$2..N]:
a[1]:= 1: found:= true:
for n from 2 while found do
  found:= false;
  for j from 1 to nops(S) do
    if ispp(a[n-1]+S[j]) then
      found:= true;
      a[n]:= S[j];
      S:= subsop(j=NULL,S);
      break
    fi
  od;
od:
seq(a[i],i=1..n-2); # Robert Israel, Apr 16 2017

Mathematica

f[s_List] := Block[{k = 1, a = s[[-1]]}, While[MemberQ[s, k] || ! PrimePowerQ[a + k], k++]; Append[s, k]]; Nest[f, {1}, 80]