A284665 Numbers of form p^i + p^j for p prime and i, j > 0.

4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 40, 46, 48, 50, 54, 56, 58, 62, 64, 66, 68, 72, 74, 80, 82, 84, 86, 90, 94, 96, 98, 106, 108, 118, 122, 128, 130, 132, 134, 136, 142, 144, 146, 150, 158, 160, 162, 166, 178, 182, 192, 194

Offset

1,1

Comments

All terms are even.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

24 = 2^4 + 2^3.
30 = 3^3 + 3^1 = 5^2 + 5^1.

Maple

N:= 1000: # for terms <= N
R:= {}: p:= 2:
while 2*p <= N do
  for i from 1 while 2*p*i <= N do
    for j from i do
      v:= p^i + p^j;
      if v > N then break fi;
      R:= R union {v};
  od od;
  p:= nextprime(p);
od:
sort(convert(R, list)); # Robert Israel, Apr 12 2026

Prog

(PARI) lista(limit) = my(v=vector(limit)); for(n=1, limit, forprime(p=2, n/2, for(k=1, logint(n\2, 2), for(j=k, logint(n, 2), if(n-p^k==p^j, v[n]=1, ))))); for(n=1, limit, if(v[n], print1(n", ")))

Crossrefs

Cf. A246655, A284667 (a subsequence).

Sequence in context: A325038 A360127 A111305 * A210939 A175246 A353537

Adjacent sequences: A284662 A284663 A284664 * A284666 A284667 A284668

Keyword

nonn

Author

Gionata Neri, Mar 31 2017

Status

approved