

A340640


Perfect powers such that the two immediately adjacent perfect powers have at least one largest exponent A025479 greater than 2.


3



4, 9, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 196, 225, 243, 256, 289, 324, 361, 484, 529, 576, 676, 784, 961, 1000, 1024, 1089, 1225, 1296, 1331, 1369, 1681, 1764, 2025, 2116, 2187, 2197, 2209, 2304, 2500, 2704, 2809, 3025, 3136, 3364, 3481, 3969
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OFFSET

1,1


LINKS



EXAMPLE

a(1) = 4 because the next perfect power is 8 = 2^3, i.e., its exponent is > 2.
a(2) = 9: the exponents of the neighbors 8 = 2^3 and 16 = 2^4 are both > 2.
16 is not in the sequence because both neighboring perfect powers 9 = 3^2 and 25 = 5^2 have exponents 2.
Neighbors with exponents > 2 of the next terms: a(3) = 25 (16 = 2^3), a(4) = 27 (32 = 2^5), a(5) = 32 (27 = 3^3), a(6) = 36 (32 = 2^5), a(7) = 49 (64 = 2^6), a(8) = 64 (81 = 3^4).


PROG

(PARI) a340640(limit)={my(p2=999, p1=2, n2=1, n1=4); for(n=5, limit, my(p0=ispower(n)); if(p0>1, if(p2+p0>4, print1(n1, ", ")); n2=n1; n1=n; p2=p1; p1=p0))};
a340640(5000)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



