A215411 a(0) = 0; a(n+1) = 2*a(n) + k where k = 0 if prime(n+2)/prime(n+1) > prime(n+1)/prime(n), otherwise k = 1.

0, 0, 1, 2, 5, 10, 21, 42, 84, 169, 338, 677, 1355, 2710, 5420, 10841, 21683, 43366, 86733, 173467, 346934, 693869, 1387738, 2775476, 5550953, 11101907, 22203814, 44407629, 88815258, 177630516, 355261033, 710522066, 1421044133, 2842088266, 5684176533

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Example

a(0) = 0;
a(1) =  0 because  prime(3)/prime(2) > prime(2)/prime(1) -> 5/3 > 3/2 => a(1) = 2*0 + 0= 0;
a(2) =  1 because  prime(4)/prime(3) < prime(3)/prime(2) -> 7/5 < 5/3 => a(2) = 2*0 + 1 = 1;
a(3) =  2 because  prime(5)/prime(4) > prime(4)/prime(3) -> 11/7 > 7/5 => a(3) = 2*1 + 0 = 2.

Maple

z0:=0: printf("%a, ", z0):for n from 1 to 40 do:p1:=ithprime(n):p2:=ithprime(n+1):p3:=ithprime(n+2):x:=evalf(p2/p1):y:=evalf(p3/p2):if y>x then k:=0:else k:=1:fi:z0:=2*z0 +k:printf("%a, ", z0):od:

Crossrefs

Cf. A000040, A215410.

Sequence in context: A030525 A116385 A267515 * A243988 A279811 A279751

Adjacent sequences: A215408 A215409 A215410 * A215412 A215413 A215414

Keyword

nonn

Author

Michel Lagneau, Aug 09 2012

Status

approved