A131697 Prime averages of two successive perfect prime powers.

101, 577, 677, 2203, 15877, 22501, 25609, 32401, 42061, 57601, 72901, 181501, 228211, 324901, 378229, 394393, 462409, 695581, 804709, 1664101, 1742401, 1971241, 2873029, 3062509, 3186229, 4137181, 4305661, 4347229, 4804889, 5336101, 6200269, 6502501, 7177693, 7209229

Offset: 1

Author

Tanya Khovanova, Sep 15 2007

Keywords

• nonn

Examples

			101 is the average of 81 and 121.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000961, A075455 (Prime averages of two successive perfect powers).

Programs

Mathematica

a = Select[ Range[2, 10000000], ! PrimeQ[ # ] && Length[FactorInteger[ # ]] == 1 &]; sizea = Length[a]; (a[[Select[Range[sizea - 1], PrimeQ[(a[[ # ]] + a[[ # + 1]])/2] &]]] + a[[Select[Range[sizea - 1], PrimeQ[(a[[ # ]] + a[[ # + 1]])/2] &] + 1]])/2

Extensions

More terms from Amiram Eldar, Feb 18 2022