A120941 a(n)=k-n where prime(k) is the smallest prime greater than prime(n)*prime(n+1).

3, 5, 9, 18, 30, 42, 60, 77, 113, 145, 179, 229, 262, 293, 353, 430, 487, 545, 622, 671, 737, 826, 916, 1052, 1184, 1249, 1310, 1373, 1443, 1654, 1894, 2026, 2131, 2298, 2481, 2602, 2782, 2943, 3107, 3298, 3436, 3651, 3866, 3975, 4083, 4346, 4808, 5144

Offset: 1

Author

Axel Harvey, Aug 18 2006

Keywords

• nonn

Comments

Parity of A120941: 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, ....

Examples

			The product of the 4th prime number, 7 and the 5th prime, 11, is 77; the smallest prime greater than this is the 22nd prime, 79; therefore the 4th term of the sequence is 22-4 = 18.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A000720, A006094, A074928.

Programs

Maple

f:= n -> numtheory:-pi(ithprime(n)*ithprime(n+1))+1-n:
map(f, [$1..100]); # Robert Israel, Mar 21 2017

Mathematica

Table[PrimePi[Prime[n]Prime[n + 1]] - n + 1, {n, 48}] (* Zak Seidov, Aug 21 2006 *)

PARI

for(n=1, 100, print1(primepi(prime(n)*prime(n + 1)) - n + 1, ", ")) \\ Indranil Ghosh, Mar 22 2017

Python

from sympy import prime, primepi
print([primepi(prime(n)*prime(n + 1)) - n + 1 for n in range(1, 100)]) # Indranil Ghosh, Mar 22 2017

Formula

a(n) = A000720(A006094(n)) + 1 - n. - Robert Israel, Mar 21 2017

Extensions

More terms from Robert G. Wilson v, Aug 21 2006