A340586 Perfect powers such that the two immediately adjacent perfect powers both have a largest exponent A025479 equal to 2.

8, 16, 169, 216, 343, 400, 441, 512, 625, 729, 841, 900, 1156, 1444, 1521, 1600, 1728, 1849, 1936, 2048, 2401, 2601, 2744, 2916, 3125, 3249, 3375, 3600, 3721, 3844, 4096, 4356, 4489, 4624, 4761, 4913, 5184, 5329, 5476, 5625, 5832, 6084, 6241, 6561, 6859, 7056

Offset: 1

Author

Hugo Pfoertner, Jan 14 2021

Keywords

• nonn

Examples

			a(1) = 8 because its neighboring perfect powers 4 = 2^2 and 9 = 3^2 both have the largest exponent 2.
9 is not in the sequence because both exponents of the neighboring perfect powers 8 = 2^3 and 16 = 2^4 are > 2.
a(2) = 16: neighbors 9 = 3^2 and 25 = 5^2 satisfy the exponent condition.
Next excluded terms: 25 (16 = 2^4, 27 = 3^3), 27 (32 = 2^5), 32 (27 = 3^3), 36 (32 = 2^5), 49 (64 = 2^6), 64 (81 = 3^4), 81 (64 = 2^6), 100 (81 = 3^4), 121 (125 = 5^3), 125 (128 = 2^7), 128 (125 = 5^3), 144 (128 = 2^7).
a(3) = 169: neighbors 144 = 12^2 and 196 = 14^2 satisfy the exponent condition.
		

Crossrefs

Cf. A000290, A001597, A025479, A111245, A153158, A340587, A340640, A340641.

Programs

PARI

a340586(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))};
a340586(7500)