OFFSET

1,1

EXAMPLE

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.

PROG

(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)

CROSSREFS

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 14 2021

STATUS

approved