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A273356 Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes. 1

%I

%S 913638,2763882,4500492,6220518,6473148,13884468,15131982,15729942,

%T 19671930,20494602,21372888,23791350,25541028,29535348,30787788,

%U 30906768,32085372,34128168,34139802,34550430,35989980,37473180,37784310,38106372

%N Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes.

%C This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.

%C The terms ending in 0 belong to A249674 (divisible by 30).

%C The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.

%C The numbers n - 49 and n + 1 belong to A134123 (p such that p + 48 is the next prime).

%C The numbers n - 49 and n -­ 1 belong to A062284 (p and p + 50 are primes).

%H Karl V. Keller, Jr., <a href="/A273356/b273356.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%e 913638 is the average of the four consecutive primes 913589, 913637, 913639, 913687.

%e 2763882 is the average of the four consecutive primes 2763833, 2763881, 2763883, 2763931.

%o (Python)

%o from sympy import isprime,prevprime,nextprime

%o for i in range(0,60000001,6):

%o ..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-49 and nextprime(i+1) == i+49: print (i,end=', ')

%o (PARI) is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-49 && nextprime(n+2)==n+49 \\ _Charles R Greathouse IV_, Jun 08 2016

%Y Cf. A014574, A077800 (twin primes), A249674, A256753.

%K nonn

%O 1,1

%A _Karl V. Keller, Jr._, May 20 2016

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Last modified April 26 08:05 EDT 2019. Contains 322472 sequences. (Running on oeis4.)