A118336 a(n) = greatest multiple of (p(n+1) - p(n)) which is < p(n), where p(m) is the m-th prime.

1, 2, 4, 4, 10, 12, 16, 16, 18, 28, 30, 36, 40, 40, 42, 48, 58, 60, 64, 70, 72, 76, 78, 88, 96, 100, 100, 106, 108, 112, 124, 126, 136, 130, 148, 150, 156, 160, 162, 168, 178, 180, 190, 192, 196, 192, 204, 220, 226, 228, 228, 238, 240, 246, 252, 258, 268, 270, 276

Offset: 1

Author

Leroy Quet, Apr 25 2006

Keywords

• nonn

Comments

A118335(n) - a(n) = 2*(p(n+1) - p(n)). A113709(n) - a(n) = p(n+1) - p(n), for n >= 2.

Crossrefs

Cf. A113709, A118335.

Programs

Maple

a:=n->(ithprime(n+1)-ithprime(n))*floor(ithprime(n)/(ithprime(n+1)-ithprime(n))): 1,seq(a(n),n=2..64); # Emeric Deutsch, Apr 27 2006

Mathematica

Join[{1},Floor[First[#]/(Last[#]-First[#])](Last[#]-First[#])&/@Partition[Prime[ Range[ 2,60]],2,1]] (* Harvey P. Dale, Feb 25 2013 *)

Formula

a(1)=1; a(n) = (p(n+1) - p(n))*floor(p(n)/(p(n+1)-p(n))) for n >= 2. - Emeric Deutsch, Apr 27 2006

Extensions

More terms from Emeric Deutsch, Apr 27 2006