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

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