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A273101 Numbers n such that n - 43, n - 1, n + 1, n + 43 are consecutive primes.

%I A273101 #19 May 22 2025 10:21:44
%S A273101 7714800,8126820,8341260,8646060,9200880,9422970,13224270,13597920,
%T A273101 14012460,14124630,15305700,17008680,17563920,18830940,22603740,
%U A273101 22812150,24576240,25197300,26147040,26196900,26932950,27225240,30305580,31214640
%N A273101 Numbers n such that n - 43, n - 1, n + 1, n + 43 are consecutive primes.
%C A273101 This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
%C A273101 The numbers n - 43 and n + 1 belong to A272176 (p and p + 44 are primes) and A134120 (p such that p + 42 is the next prime).
%C A273101 The numbers n - 43 and n - 1 belong to A271982 (p and p + 42 are primes).
%H A273101 Charles R Greathouse IV, <a href="/A273101/b273101.txt">Table of n, a(n) for n = 1..10000</a>
%H A273101 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A273101 7714800 is the average of the four consecutive primes 7714757, 7714799, 7714801, 7714843.
%e A273101 8126820 is the average of the four consecutive primes 8126777, 8126819, 8126821, 8126863.
%o A273101 (Python)
%o A273101 from sympy import isprime,prevprime,nextprime
%o A273101 for i in range(0,60000001,6):
%o A273101   if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-43 and nextprime(i+1) == i+43: print (i,end=', ')
%o A273101 (PARI) is(n)=n%30==0 && isprime(n-1) && isprime(n+1) && nextprime(n+2)==n+43 && precprime(n-2)==n-43 \\ _Charles R Greathouse IV_, May 15 2016
%Y A273101 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A273101 nonn
%O A273101 1,1
%A A273101 _Karl V. Keller, Jr._, May 15 2016