A340640 Perfect powers such that the two immediately adjacent perfect powers have at least one largest exponent A025479 greater than 2.
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
Offset: 1
Keywords
Examples
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).
Programs
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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)