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A273356 Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes. 1
913638, 2763882, 4500492, 6220518, 6473148, 13884468, 15131982, 15729942, 19671930, 20494602, 21372888, 23791350, 25541028, 29535348, 30787788, 30906768, 32085372, 34128168, 34139802, 34550430, 35989980, 37473180, 37784310, 38106372 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

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

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

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

LINKS

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

EXAMPLE

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

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

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-49 and nextprime(i+1) == i+49: print (i, end=', ')

(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

CROSSREFS

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

Sequence in context: A236617 A237155 A112688 * A253991 A253998 A258908

Adjacent sequences:  A273353 A273354 A273355 * A273357 A273358 A273359

KEYWORD

nonn

AUTHOR

Karl V. Keller, Jr., May 20 2016

STATUS

approved

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Last modified March 26 00:20 EDT 2019. Contains 321478 sequences. (Running on oeis4.)