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%I #31 Sep 08 2022 08:46:12
%S 30,60,270,570,600,1230,1290,1620,2340,2550,3540,4020,4650,5850,6270,
%T 6360,6570,10860,11490,14550,15270,17490,19080,19380,19470,23670,
%U 26730,29130,32370,34260,41610,48480,49200,49530,51420,51480
%N Numbers n such that n is the average of four consecutive primes n-7, n-1, n+1 and n+7.
%C This sequence is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30*n).
%H Karl V. Keller, Jr., <a href="/A258879/b258879.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>
%F a(n) = A078854(n) + 7.
%e For n=30: 23, 29, 31, 37 are consecutive primes (n-7=23, n-1=29, n+1=31, n+7=37).
%e For n=60: 53, 59, 61, 67 are consecutive primes (n-7=53, n-1=59, n+1=61, n+7=67).
%t Select[ 5 Range@ 11000, PrimeQ[# - 7] && PrimeQ[# - 1] && PrimeQ[# + 1] && PrimeQ[# + 7] &] (* _Robert G. Wilson v_, Jun 28 2015 *)
%o (Python)
%o from sympy import isprime,prevprime,nextprime
%o for i in range(0,10001,2):
%o ..if isprime(i-1) and isprime(i+1):
%o ....if prevprime(i-1) == i-7 and nextprime(i+1) == i+7 : print (i,end=', ')
%o (Magma) [n: n in [13..2*10^5] | IsPrime(n-7) and IsPrime(n-1) and IsPrime(n+1) and IsPrime(n+7)]; // _Vincenzo Librandi_ Jul 16 2015
%o (PARI) main(size)={my(v=vector(size),i,t=8);for(i=1,size,while(1,if(isprime(t-7)&&isprime(t-1)&&isprime(t+1)&&isprime(t+7),v[i]=t;break,t++));t++);return(v);} /* _Anders Hellström_, Jul 17 2015 */
%Y Cf. A014574, A077800 (twin primes), A078854, A249674, A256753.
%K nonn
%O 1,1
%A _Karl V. Keller, Jr._, Jun 13 2015
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