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
A054680
n consecutive primes differ by a multiple of 8 starting at a(n).
Original entry on oeis.org
89, 1823, 20809, 73133, 989647, 3250469, 9065867, 35677501, 101341613, 1383423311, 11312238283, 19201563659, 132932904029, 534956098463, 925195153703, 20151469541389, 20151469541389, 102573904861013
Offset: 2
More terms from Larry Reeves (larryr(AT)acm.org), Nov 09 2000
More terms from Larry Soule (lsoule(AT)gmail.com), Jun 11 2006
A162865
Initial prime of exactly nine consecutive primes congruent to 1 modulo 4.
Original entry on oeis.org
11593, 206953, 315257, 541097, 906541, 992393, 1124993, 1410361, 1595081, 1781569, 1872049, 2043329, 2090353, 2312749, 2381657, 2481509, 2497289, 2718389, 2758109, 2772409, 2976397, 3863473, 3868849, 4027957, 4042673, 4375141, 4464841, 4547581, 4606153
Offset: 1
-
m9Q[l_]:=Module[{ms=Mod[l,4]},First[ms]!=1&&Last[ms]!=1&&Union[Take[ ms,{2,10}]]=={1}]; Transpose[Select[Partition[ Prime[Range[ 290000]], 11,1],m9Q]][[2]] (* Harvey P. Dale, Oct 23 2011 *)
A162866
Initial prime of exactly nine consecutive primes congruent to 3 modulo 4.
Original entry on oeis.org
39607, 278051, 339863, 341827, 402371, 519587, 735211, 919423, 1123219, 1191643, 1263239, 1329763, 1635547, 1648919, 1737863, 1994119, 2191687, 2465227, 2566279, 3025423, 3101743, 3197899, 3306731, 3719467, 4259243, 4466411, 4498883, 4591507, 4680503, 5031863
Offset: 1
-
m9Q[l_]:=Module[{ms=Mod[l,4]},First[ms]!=3&&Last[ms]!=3&&Union[ Take[ ms,{2,10}]]=={3}]; Transpose[Select[Partition[Prime[Range[ 320000]], 11,1],m9Q]][[2]] (* Harvey P. Dale, Oct 23 2011 *)
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.
-
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
A054694
n consecutive primes differ by 8 or more starting at a(n).
Original entry on oeis.org
89, 199, 683, 683, 683, 1789, 13469, 13469, 13469, 13469, 62687, 62687, 62687, 62687, 200597, 200597, 568441, 568441, 568441, 568441, 568441, 1974079, 3036799, 3059453, 3059453, 3059453, 5949347, 5949347, 5949347, 5949347
Offset: 2
-
With[{prs=Prime[Range[500000]]},Table[SelectFirst[Partition[prs,n,1],Min[ Differences[ #]]>7&][[1]],{n,2,35}]] (* Harvey P. Dale, Sep 03 2021 *)
More terms from Larry Reeves (larryr(AT)acm.org), Nov 09 2000
Showing 1-6 of 6 results.
Comments