A054678
n consecutive primes differ by a multiple of 4 starting at a(n).
Original entry on oeis.org
7, 89, 199, 463, 463, 463, 11593, 11593, 183091, 241603, 241603, 241603, 9177431, 9177431, 12270077, 105639091, 297779117, 297779117, 727334879, 1113443017, 1113443017, 1113443017, 1113443017, 79263248027, 84676452781, 113391385603
Offset: 2
More terms from Larry Reeves (larryr(AT)acm.org), Nov 09 2000
A054679
First of n consecutive primes which differ by a multiple of 6.
Original entry on oeis.org
2, 23, 47, 251, 1741, 1741, 19471, 118801, 148531, 148531, 406951, 1820111, 2339041, 19725473, 19725473, 73451737, 232301497, 400414121, 489144599, 489144599, 766319189, 766319189, 21549657539, 21549657539, 21549657539, 140432294381, 140432294381, 437339303279, 1552841185921, 1552841185921, 1552841185921
Offset: 1
More terms from Larry Reeves (larryr(AT)acm.org), Nov 09 2000
Initial term and a(27)-a(31) added and name edited by
M. F. Hasler, Sep 02 2016
A259360
Initial prime in the least set of exactly n+1 consecutive primes with n gaps all multiples of 4.
Original entry on oeis.org
7, 89, 199, 883, 12401, 463, 36551, 11593, 183091, 766261, 3358169, 241603, 11739307, 9177431, 12270077, 105639091, 310523021, 297779117, 727334879, 5344989829, 1481666377, 2572421893, 1113443017, 79263248027, 84676452781
Offset: 1
a(6)=463 because the first set of 7 consecutive primes is {463,467,479,487,491,499,503} with 6 gaps {4,12,8,4,8,4} all multiples of 4 while the next prime after 503 is 509 and 509-503=6 is not a multiple of 4.
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back(p,n)=while(n,p=precprime(p-1); n--); p
v=vector(20); g=0; p=2; forprime(q=3,1e6, if((q-p)%4, if(g&&g<=#v&&v[g]==0, v[g]=back(p,g)); g=0, g++);p=q); v \\ Charles R Greathouse IV, Jul 14 2015
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