A064799 Sum of n-th prime number and n-th composite number.

6, 9, 13, 16, 21, 25, 31, 34, 39, 47, 51, 58, 63, 67, 72, 79, 86, 89, 97, 103, 106, 113, 118, 125, 135, 140, 143, 149, 153, 158, 173, 179, 186, 189, 200, 203, 211, 218, 223, 230, 237, 241, 253, 256, 261, 264, 277, 291, 296, 299, 305, 313, 316, 327, 334, 341

Offset: 1

Author

Konstantin Knop, Oct 21 2001

Keywords

• nonn
• easy

Examples

			a(1)=6 because the first prime is 2 and the first composite is 4; 2 + 4 = 6
a(2)=9 because prime(2)=3 and composite(2)=6; 3 + 6 = 9.
		

References

• Ivan Grischenko, ivansasha(AT)mtu-net.ru, private communication.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002808, A171639.

Programs

Mathematica

Module[{nn=100,cmps},cmps=Select[Range[nn],CompositeQ];Total/@Thread[{Prime[Range[ Length[ cmps]]],cmps}]] (* Harvey P. Dale, Mar 31 2024 *)

PARI

nextComp(n)= { if (!isprime(n), return(n)); return(n + 1) }
{ p=1; c=3; for (n=1, 100, p=nextprime(p + 1); c=nextComp(c + 1); print1(p + c, ", ") ) } \\ Harry J. Smith, Sep 25 2009

Python

from sympy import prime, composite
def A064799(n): return prime(n)+composite(n) # Chai Wah Wu, Aug 30 2021

Formula

a(n) = prime(n) + composite(n).

From Jaroslav Krizek, Dec 13 2009: (Start)

a(n) = A000040(n) + A002808(n).

a(n) = A171639(n+1). (End)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Nov 12 2001

Offset changed from 0 to 1 by Harry J. Smith, Sep 25 2009