A108301 Digital sum of the Fermat number 2^(2^n) + 1.

3, 5, 8, 14, 26, 59, 89, 167, 377, 734, 1376, 2741, 5624, 11120, 22166, 44222, 88262, 176180, 353042, 707648, 1419974, 2836751, 5679620, 11365592, 22723865, 45445442, 90899234, 181828850

Offset: 0

Author

Jason Earls, Jun 29 2005

Keywords

• base
• nonn

Comments

a(0), a(1), a(5), a(6), a(7) and a(11) are primes. Are there any more?

Examples

			a(5)=59 because 2^(2^5) + 1 = 4294967297 and the sum of those decimal digits is 59.
		

Crossrefs

Cf. A000215.

Programs

Maple

a:=proc(n) local nn, z: nn:=convert(2^(2^n)+1,base,10): z:=nops(nn): add(nn[j],j=1..z) end: seq(a(n),n=0..22); # Emeric Deutsch

Mathematica

f[n_] := Plus @@ IntegerDigits[2^(2^n)] + 1; Table[ f[n], {n, 0, 27}] (* Robert G. Wilson v, Jul 02 2005 *)

Formula

a(n) = ~4.5*A057755. - Robert G. Wilson v, Jul 02 2005

Extensions

More terms from Emeric Deutsch and Robert G. Wilson v, Jul 02 2005