A161164 - OEIS

%I #11 Jan 18 2021 11:19:37

%S 1,18,30,36,40,50,60,54,58,56,70,68,70,86,90,66,70,104,114,96,112,108,

%T 112,98,112,116,124,134,138,126,130,128,132,110,112,108,114,90,96,92,

%U 94,30,36,36,46,26,28,22,20,60,30,52,44,54,42,54,50,52,48,178,164,168,150

%N Absolute value of (the n-th twin prime minus the n-th non-twin prime).

%F a(n) = |A001097(n)-A007510(n)|.

%e a(1)=abs(3-2)=1, a(2)=abs(5-23)=abs(-18)=18, a(3)=abs(7-37)=abs(-30)=30, etc.

%o (Python)

%o from sympy import nextprime

%o def aupton(terms):

%o   n, p, q = 1, 2, 3

%o   alst, non_twins, twins = [], [2], [3]

%o   while True:

%o     p, q = q, nextprime(q)

%o     if q - p == 2:

%o       if p != twins[-1]: twins.append(p)

%o       twins.append(q)

%o     else:

%o       if p != twins[-1]: non_twins.append(p)

%o     if len(twins) >= n and len(non_twins) >= n:

%o       alst.append(abs(twins[n-1] - non_twins[n-1]))

%o       if n == terms: break

%o       n += 1

%o   return alst

%o print(aupton(63)) # _Michael S. Branicky_, Jan 18 2021

%Y Cf. A001097, A007510.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Jun 04 2009

%E Terms corrected by _D. S. McNeil_, Dec 10 2009