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 A273101 Numbers n such that n - 43, n - 1, n + 1, n + 43 are consecutive primes. 1
 7714800, 8126820, 8341260, 8646060, 9200880, 9422970, 13224270, 13597920, 14012460, 14124630, 15305700, 17008680, 17563920, 18830940, 22603740, 22812150, 24576240, 25197300, 26147040, 26196900, 26932950, 27225240, 30305580, 31214640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753. 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). The numbers n - 43 and n -­ 1 belong to A271982(p and p + 42 are primes). LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Twin Primes EXAMPLE 7714800 is the average of the four consecutive primes 7714757, 7714799, 7714801, 7714843. 8126820 is the average of the four consecutive primes 8126777, 8126819, 8126821, 8126863. PROG (Python) from sympy import isprime, prevprime, nextprime for i in range(0, 60000001, 6): ..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-43 and nextprime(i+1) == i+43: print (i, end=', ') (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 CROSSREFS Cf. A014574, A077800 (twin primes), A249674, A256753. Sequence in context: A192105 A233597 A258954 * A124416 A320516 A319809 Adjacent sequences:  A273098 A273099 A273100 * A273102 A273103 A273104 KEYWORD nonn AUTHOR Karl V. Keller, Jr., May 15 2016 STATUS approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)