A161164 Absolute value of (the n-th twin prime minus the n-th non-twin prime).

1, 18, 30, 36, 40, 50, 60, 54, 58, 56, 70, 68, 70, 86, 90, 66, 70, 104, 114, 96, 112, 108, 112, 98, 112, 116, 124, 134, 138, 126, 130, 128, 132, 110, 112, 108, 114, 90, 96, 92, 94, 30, 36, 36, 46, 26, 28, 22, 20, 60, 30, 52, 44, 54, 42, 54, 50, 52, 48, 178, 164, 168, 150

Offset

1,2

Links

Table of n, a(n) for n=1..63.

Formula

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

Example

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

Prog

(Python)
from sympy import nextprime
def aupton(terms):
  n, p, q = 1, 2, 3
  alst, non_twins, twins = [], [2], [3]
  while True:
    p, q = q, nextprime(q)
    if q - p == 2:
      if p != twins[-1]: twins.append(p)
      twins.append(q)
    else:
      if p != twins[-1]: non_twins.append(p)
    if len(twins) >= n and len(non_twins) >= n:
      alst.append(abs(twins[n-1] - non_twins[n-1]))
      if n == terms: break
      n += 1
  return alst
print(aupton(63)) # Michael S. Branicky, Jan 18 2021

Crossrefs

Cf. A001097, A007510.

Sequence in context: A032612 A151700 A154367 * A092357 A141115 A377185

Adjacent sequences: A161161 A161162 A161163 * A161165 A161166 A161167

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 04 2009

Extensions

Terms corrected by D. S. McNeil, Dec 10 2009

Status

approved