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A259025
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Numbers n such that n is the average of four consecutive primes n-11, n-1, n+1 and n+11.
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2
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420, 1050, 2028, 2730, 3582, 4230, 4242, 4272, 4338, 6090, 6132, 6690, 6792, 8220, 11058, 11160, 11970, 12252, 15288, 19542, 19698, 21588, 21600, 26892, 27540, 28098, 28308, 29400, 30840, 30870, 31080, 32412, 42072, 45318, 47808, 48120
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OFFSET
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1,1
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COMMENTS
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This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 are congruent to 0 mod 30.
The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
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LINKS
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FORMULA
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EXAMPLE
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For n=420: 409, 419, 421, 431 are consecutive primes (n-11=409, n-1=419, n+1=421, n+11=431).
For n=1050: 1039, 1049, 1051, 1061 are consecutive primes (n-11=1039, n-1=1049, n+1=1051, n+11=1061).
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MATHEMATICA
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{p, q, r, s} = {2, 3, 5, 7}; lst = {}; While[p < 50000, If[ Differences[{p, q, r, s}] == {10, 2, 10}, AppendTo[lst, q + 1]]; {p, q, r, s} = {q, r, s, NextPrime@ s}]; lst (* Robert G. Wilson v, Jul 15 2015 *)
Mean/@Select[Partition[Prime[Range[5000]], 4, 1], Differences[#]=={10, 2, 10}&] (* Harvey P. Dale, Sep 11 2019 *)
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PROG
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(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 50001, 2):
..if isprime(i-1) and isprime(i+1):
....if prevprime(i-1) == i-11 and nextprime(i+1) == i+11 : print (i, end=', ')
(PARI) is(n)=n%6==0&&isprime(n-11)&&isprime(n-1)&&isprime(n+1)&&isprime(n+11)&&!isprime(n-7)&&!isprime(n-5)&&!isprime(n+5)&&!isprime(n+7) \\ Charles R Greathouse IV, Jul 17 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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