A102332
Initial prime p introducing a prime sextuplet of consecutive primes as follows: {p, p+10, p+18, p+28, p+36, p+46} with the corresponding prime-difference-pattern is {10,8,10,8,10}.
Original entry on oeis.org
37861, 39181, 324763, 692743, 810391, 945331, 1047961, 1429573, 1513573, 1540813, 1799071, 3463573, 3861223, 3979201, 4536121, 4641001, 5154343, 5445403, 5874853, 7851583, 8820793, 8961373, 8976403, 9302113, 9673351, 10323133, 11074033, 11136883, 11899333, 13505983
Offset: 1
Cf.
A001223,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A047078,
A067140,
A067141.
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tm=TimeUsed[];ta={{0}};Do[g=n;d1=10;d2=8;d3=10;d4=8;d5=10; s1=Prime[n+1]-Prime[n];s2=Prime[n+2]-Prime[n+1]; s3=Prime[n+3]-Prime[n+2];s4=Prime[n+4]-Prime[n+3]; s5=Prime[n+5]-Prime[n+4];If[Equal[s1, d1]&&Equal[s2, d2]&& Equal[s3, d3]&&Equal[s4, d4]&&Equal[s5, d5], Print[{Prime[n], s1, s2, s3, s4, s5}];ta=Append[ta, Prime[n]]], {n, 1, 10000000}] {ta=Delete[ta, 1], {d1, d2}} {g, TimeUsed[]-tm}
Transpose[Select[Partition[Prime[Range[650000]],6,1],Differences[#]=={10,8,10,8,10}&]][[1]] (* Harvey P. Dale, Oct 18 2013 *)
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list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 10 && p3 - p2 == 8 && p4 - p3 == 10 && p5 - p4 == 8 && p6 - p5 == 10, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6);} \\ Amiram Eldar, Feb 18 2025
A067141
Primes p beginning consecutive prime-difference pattern as follows: p, (16, 2, 16, 2), p+36.
Original entry on oeis.org
225733, 819373, 830293, 856993, 895633, 924793, 1138393, 1210003, 1214623, 1353223, 1526053, 2051443, 2183773, 2298853, 2345443, 3169723, 3254773, 3287293, 3539743, 3675613, 3847603, 4630063, 4633003, 5137003, 5238403
Offset: 1
First term a(1)=p(20082)=225773; it is followed by 225789, 225791, 225807, 225809=p(20086) primes, where the 4 corresponding consecutive differences equal {16, 2, 16, 2}. See analogous cases A022008, A067140.
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d[x_] := Prime[x+1]-Prime[x] Do[If[Equal[d[n], 16]&&Equal[d[n+1], 2]&& Equal[d[n+2], 16]&&Equal[d[n+3], 2], k=k+1; Print[Prime[n]]], {n, 1, 10000000}]
Select[Partition[Prime[Range[400000]],5,1],Differences[#]=={16,2,16,2}&][[All,1]] (* Harvey P. Dale, Jan 01 2018 *)
A102333
Initial terms of quartets of consecutive primes as follows: {p, p+16, p+24, p+40}. The corresponding difference-pattern is {16,8,16}.
Original entry on oeis.org
108247, 121507, 166783, 169567, 178207, 216133, 257053, 258763, 272863, 274123, 372613, 383533, 384343, 396157, 413143, 501577, 562477, 577153, 581353, 635293, 721267, 727273, 738937, 769903, 908113, 917713, 932497, 937903, 965467, 980377, 989647, 1008547, 1126537
Offset: 1
Cf.
A001223,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A052378,
A067140,
A067141,
A102332.
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Transpose[Select[Partition[Prime[Range[78000]],4,1],Differences[#] == {16,8,16}&]][[1]] (* Harvey P. Dale, Mar 18 2012 *)
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list(lim) = {my(p1 = 2, p2 = 3, p3 = 5); forprime(p4 = 7, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4);} \\ Amiram Eldar, Feb 18 2025
A102334
Initial terms of quintuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48}. The corresponding difference-pattern is {16,8,16,8}.
Original entry on oeis.org
272863, 274123, 372613, 1394893, 1634293, 2380423, 3846373, 5298523, 5358013, 5797903, 6741913, 7554823, 7647643, 7716103, 7738153, 8241463, 8358283, 9710473, 9859783, 12454333, 12510193, 12796423, 13710133, 14477893, 15162493, 15186583, 15263503, 15603853, 16438243, 16771933, 17913283, 18957973, 19373623
Offset: 1
Cf.
A001223,
A022007,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A052378,
A067140,
A067141,
A102332,
A102333.
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Select[Partition[Prime[Range[1233300]], 5, 1], Differences[#] == {16, 8, 16, 8} &][[;;, 1]] (* Amiram Eldar, Feb 18 2025 *)
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list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 18 2025
Missing terms a(1)-a(11) inserted by
Amiram Eldar, Feb 18 2025
A102335
Initial terms of sextuplets of consecutive primes as follows: {p, p+16, p+24, p+40, p+48, p+64}. The corresponding difference-pattern is {16,8,16,8,16}.
Original entry on oeis.org
12454333, 21228553, 25131193, 38589673, 41426353, 46254253, 56564623, 60498133, 61151863, 96691213, 158497153, 169760713, 182960473, 201513133, 226086283, 236031463, 253806913, 290686483, 305472373, 344550643, 369110983, 380973253, 421335883, 445537333, 461955763
Offset: 1
Cf.
A001223,
A022008,
A052162,
A052163,
A052164,
A052165,
A052166,
A052167,
A052168,
A052378,
A067140,
A067141,
A102332,
A102333,
A102334.
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Transpose[Select[Partition[Prime[Range[20000000]],6,1],Differences[#] == {16,8,16,8,16}&]][[1]] (* Harvey P. Dale, Nov 08 2011 *)
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list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7, p5 = 11); forprime(p6 = 13, lim, if(p2 - p1 == 16 && p3 - p2 == 8 && p4 - p3 == 16 && p5 - p4 == 8 && p6 - p5 == 16, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5; p5 = p6);} \\ Amiram Eldar, Feb 18 2025
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