|
%I #12 Dec 04 2020 00:25:47
%S 90438,258918,293862,385740,426162,532950,1073952,1317192,1318410,
%T 1401318,1565382,1894338,1986168,2174772,2612790,2764788,3390900,
%U 3450048,3618960,3797250,3961722,3973062,4074870,4306230,4648068,4917360,5351010,5460492
%N Numbers n such that n - 31, n - 1, n + 1 and n + 31 are consecutive primes.
%C This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
%C The terms ending in 0 are divisible by 30 (cf. A249674).
%C The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.
%C The numbers n - 31 and n + 1 belong to A049481 (p and p + 30 are primes) and A124596 (p where p + 30 is the next prime).
%C The numbers n - 31 and n - 1 belong to A049489 (p and p + 32 are primes).
%H Karl V. Keller, Jr., <a href="/A270754/b270754.txt">Table of n, a(n) for n = 1..100000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e 90438 is the average of the four consecutive primes 90407, 90437, 90439, 90469.
%e 258918 is the average of the four consecutive primes 258887, 258917, 258919, 258949.
%o (Python)
%o from sympy import isprime,prevprime,nextprime
%o for i in range(0,1000001,6):
%o .. if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-31 and nextprime(i+1) == i+31 : print (i,end=', ')
%Y Cf. A014574, A077800 (twin primes), A249674, A256753.
%K nonn
%O 1,1
%A _Karl V. Keller, Jr._, Mar 22 2016
|
