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%I #22 May 09 2021 04:58:04
%S 3,5,9,18,30,42,60,77,113,145,179,229,262,293,353,430,487,545,622,671,
%T 737,826,916,1052,1184,1249,1310,1373,1443,1654,1894,2026,2131,2298,
%U 2481,2602,2782,2943,3107,3298,3436,3651,3866,3975,4083,4346,4808,5144
%N a(n)=k-n where prime(k) is the smallest prime greater than prime(n)*prime(n+1).
%C 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, ....
%H Robert Israel, <a href="/A120941/b120941.txt">Table of n, a(n) for n = 1..4000</a>
%F a(n) = A000720(A006094(n)) + 1 - n. - _Robert Israel_, Mar 21 2017
%e 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.
%p f:= n -> numtheory:-pi(ithprime(n)*ithprime(n+1))+1-n:
%p map(f, [$1..100]); # _Robert Israel_, Mar 21 2017
%t Table[PrimePi[Prime[n]Prime[n + 1]] - n + 1, {n, 48}] (* _Zak Seidov_, Aug 21 2006 *)
%o (PARI) for(n=1, 100, print1(primepi(prime(n)*prime(n + 1)) - n + 1, ", ")) \\ _Indranil Ghosh_, Mar 22 2017
%o (Python)
%o from sympy import prime, primepi
%o print([primepi(prime(n)*prime(n + 1)) - n + 1 for n in range(1, 100)]) # _Indranil Ghosh_, Mar 22 2017
%Y Cf. A000720, A006094, A074928.
%K nonn
%O 1,1
%A _Axel Harvey_, Aug 18 2006
%E More terms from _Robert G. Wilson v_, Aug 21 2006
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