A290162
Initial primes of 8 consecutive primes with 7 consecutive gaps 14, 12, 10, 8, 6, 4, 2.
Original entry on oeis.org
5647457, 18117977, 21705503, 32465063, 37091597, 57269633, 90217163, 109933673, 111053573, 124123133, 145594583, 146742863, 163123997, 200416343, 239659907, 245333267, 272213813, 335971367, 350795033, 470838833, 701465327, 749927357, 888801707, 1060690667
Offset: 1
Prime(390215..390222) = {5647457, 5647471, 5647483, 5647493, 5647501, 5647507, 5647511, 5647513} and 5647457 + 14 = 5647471, 5647471 + 12 = 5647483, 5647483 + 10 = 5647493, 5647493 + 8 = 5647501, 5647501 + 6 = 5647507, 5647507 + 4 = 5647511, 5647511 + 2 = 5647513.
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P:=Filtered([1..100000000],IsPrime);; I:=Reversed([2,4,6,8,10,12,14]);;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);; Collected(last);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4],P1[i+5],P1[i+6]]);;
P3:=List(Positions(P2,I),i->P[i]); Length(P3);
A286891
Initial primes of 6 consecutive primes with 5 consecutive gaps 10, 8, 6, 4, 2.
Original entry on oeis.org
41203, 556243, 576193, 715849, 752263, 859249, 891799, 1107763, 1191079, 1201999, 1210369, 1510189, 1601599, 1893163, 2530963, 2678719, 2881243, 3257689, 3431479, 3545263, 3792949, 3804919, 4041109, 4479463, 4867309
Offset: 1
Prime(4313..4318) = {41203, 41213, 41221, 41227, 41231, 41233} and 41203 + 10 = 41213, 41213 + 8 = 41221, 41221 + 6 = 41227, 41227 + 4 = 41231, 41231 + 2 = 41233.
Also, prime(68287..68292) = {859249, 859259, 859267, 859273, 859277, 859279} and 859249 + 10 = 859259, 859259 + 8 = 859267, 859267 + 6 = 859273, 859273 + 4 = 859277, 859277 + 2 = 859279.
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P:=Filtered([1..20000000],IsPrime);; I:=Reversed([2,4,6,8,10]);;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4]]);;
P3:=List(Positions(P2,I),i->P[i]);
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K:=10^7: # to get all terms <= K.
Primes:=select(isprime,[seq(i,i=3..K+30,2)]): Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1], Primes[t+3]-Primes[t+2], Primes[t+4]-Primes[t+3], Primes[t+5]-Primes[t+4]]=[10,8,6,4,2], [$1..nops(Primes)-5])]; # Muniru A Asiru, Aug 15 2017
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Select[Partition[Prime[Range[340000]],6,1],Differences[#]=={10,8,6,4,2}&][[All,1]] (* Harvey P. Dale, Aug 22 2018 *)
A290264
Initial primes of 9 consecutive primes with 8 consecutive gaps 16, 14, 12, 10, 8, 6, 4, 2.
Original entry on oeis.org
32465047, 37091581, 146742847, 239659891, 245333251, 272213797, 1060690651, 1541736811, 2002738207, 2480351677, 2636566351, 4421955007, 6168859201, 8158683037, 10367633527, 10623394321, 11452116817, 11691059641, 11892876841, 13551877831, 15043908637
Offset: 1
32465047 is a member of this sequence because the 9 consecutive primes 32465047, 32465063, 32465077, 32465089, 32465099, 32465107, 32465113, 32465117, 32465119 have consecutive gaps 16, 14, 12, 10, 8, 6, 4, 2. That is, 32465047 + 16 = 32465063, 32465063 + 14 = 32465077, 32465077 + 12 = 32465089, 32465089 + 10 = 32465099, 32465099 + 8 = 32465107, 32465107 + 6 = 32465113, 32465113 + 4 = 32465117, 32465117 + 2 = 32465119.
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P:=Filtered([1..50000000],IsPrime);;I:=Reversed([2,4,6,8,10,12,14,16]);;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);; Collected(last);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3],P1[i+4],P1[i+5],P1[i+6],P1[i+7]]);;
P3:=List(Positions(P2,I),i->P[i]); Length(P3);
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