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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjectured to be a permutation of the natural numbers.

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

EXAMPLE

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.

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]

CROSSREFS

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

Sequence in context: A140595 A187098 A187099 * A063932 A323785 A327626

Adjacent sequences:  A284046 A284047 A284048 * A284050 A284051 A284052

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 19 2017

STATUS

approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)