A377933 First differences of consecutive perfect powers m^k with k>=3 (A076467).

7, 8, 11, 5, 32, 17, 44, 3, 88, 27, 13, 87, 169, 113, 104, 271, 24, 272, 35, 397, 320, 139, 10, 204, 343, 381, 250, 721, 817, 919, 729, 298, 917, 224, 192, 1069, 739, 648, 1519, 1657, 817, 984, 759, 423, 769, 2107, 1053, 1216, 2437, 2611, 1561, 1230, 2977, 3169, 2479, 888

Offset: 1

Author

Hugo Pfoertner, Nov 24 2024

Keywords

• nonn
• easy

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000
• Plot of log_10(a(n)) vs log_10(n), using Plot 2.

Crossrefs

Cf. A001597, A053289, A076467.

Programs

Maple

N:= 10^5: # for terms <= N of A076467
S:= sort(convert({1, seq(seq(m^k, m = 2 .. floor(N^(1/k))), k=3..ilog2(N))},list)):
S[2..-1]-S[1..-2]; # Robert Israel, Nov 24 2024

PARI

lista(nn) = my(S=List(1)); for(x=2, sqrtnint(nn, 3), for(k=3, logint(nn, x), listput(S, x^k))); my(v=Set(S)); vector(#v-1, k, v[k+1]-v[k]); \\ Michel Marcus, Nov 24 2024

Formula

a(n) = A076467(n+1) - A076467(n).