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 A262668 Numbers n such that n-19, n-1, n+1 and n+19 are consecutive primes. 1
 20982, 28182, 51768, 57222, 76422, 87720, 90678, 104850, 108108, 110730, 141180, 199602, 227112, 248118, 264600, 268842, 304392, 304458, 320082, 322920, 330018, 382728, 401670, 414432, 429972, 450258, 467082, 489408, 520548, 535608, 540120 (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 are divisible by 30 (cf. A249674). The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively. LINKS Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Twin Primes EXAMPLE 20982 is the average of the four consecutive primes 20963, 20981, 20983, 21001. 28182 is the average of the four consecutive primes 28163, 28181, 28183, 28201. MATHEMATICA Select[Range[6, 600000, 6], And[AllTrue[{# - 1, # + 1}, PrimeQ], NextPrime[# - 1, -1] == # - 19, NextPrime[# + 1] == # + 19] &] (* Michael De Vlieger, Sep 27 2015, Version 10 *) Select[Prime@Range@60000, NextPrime[#, {1, 2, 3}] == {18, 20, 38} + # &] + 19 (* Vincenzo Librandi, Oct 10 2015 *) Mean/@Select[Partition[Prime[Range[50000]], 4, 1], Differences[#]=={18, 2, 18}&] (* Harvey P. Dale, Jan 16 2019 *) PROG (Python) from sympy import isprime, prevprime, nextprime for i in range(0, 1000001, 6): ..if isprime(i-1) and isprime(i+1): ....if prevprime(i-1) == i-19 and nextprime(i+1) == i+19 : print(i, end=', ') CROSSREFS Cf. A014574, A077800 (twin primes), A249674, A256753. Sequence in context: A188104 A278903 A233649 * A344354 A344355 A231314 Adjacent sequences:  A262665 A262666 A262667 * A262669 A262670 A262671 KEYWORD nonn AUTHOR Karl V. Keller, Jr., Sep 26 2015 STATUS approved

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Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)