A069496
Smaller member of a twin prime pair with a square sum.
Original entry on oeis.org
17, 71, 881, 1151, 2591, 3527, 4049, 15137, 20807, 34847, 46817, 69191, 83231, 103967, 112337, 149057, 176417, 179999, 206081, 281249, 362951, 388961, 438047, 472391, 478241, 538721, 649799, 734471, 808991, 960497, 1080449, 1143071
Offset: 1
71 is a term as the smaller member of the twin prime pair (71,73) as 71+73 = 144 = 12^2.
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isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):
select(isa, [$4..1000000]); # Peter Luschny, Jan 05 2020
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First/@Select[Partition[Prime[Range[9*10^4]],2,1],Differences[#]=={2} && IntegerQ[Sqrt[Total[#]]] &] (* Jayanta Basu, May 26 2013 *)
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t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e4, if(issquare(2*t(n)+2), print1(t(n), ", "))); \\ Altug Alkan, Mar 14 2016
A245591
Cubes which are the sum of twin prime pairs.
Original entry on oeis.org
8, 216, 5268024, 59319000, 114791256, 209584584, 543338496, 970299000, 1137893184, 1177583616, 1505060136, 1728000000, 4065356736, 5545233000, 5890514616, 7011739944, 8947094976, 9340607016, 10941048000, 13824000000, 14996130696, 17293606056, 17657244864, 17902480896, 20480864256
Offset: 1
3 and 5 are twin primes and 3 + 5 = 8 = 2^3. So 8 is a member of this sequence.
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a(N) = for(n=1,N,p=n^3;if(nextprime(p/2)-precprime(p/2)==2&&precprime(p/2)+nextprime(p/2)==p,print1(p,", "))) \\ vary the program's range for any N
A119767
Perfect powers which are the sum of twin prime pairs.
Original entry on oeis.org
8, 36, 144, 216, 1764, 2304, 5184, 7056, 8100, 30276, 41616, 69696, 93636, 138384, 166464, 207936, 224676, 279936, 298116, 352836, 360000, 412164, 562500, 725904, 777924, 876096, 944784, 956484, 1077444, 1299600, 1468944, 1617984, 1920996, 2160900, 2286144, 2304324, 2509056
Offset: 1
8 = 2^3 = 3 + 5 (twin primes). Thus 8 is a member of this sequence.
36 = 6^2 = 17 + 19 (twin primes). Thus 36 is a member of this sequence.
a(3) = 71 + 73 = 144.
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egcd := proc(n::nonnegint) local L; if n=0 or n=1 then n else L:=ifactors(n)[2]; L:=map(z->z[2],L); igcd(op(L)) fi end: L:=[]: for w to 1 do for x from 1 to 2*12^2 do s:=6*x; for r from 2 to 79 do t:=s^r; if egcd(s)=1 and andmap(isprime,[(t-2)/2,(t+2)/2]) then print((t-2)/2,(t+2)/2,t)); L:=[op(L),[(t-2)/2,(t+2)/2,t]]; fi; od od od; L:=sort(L,(a,b)->a[1]z[3],L);
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Lim=2600000;ts=Select[Prime[Range[PrimePi[Lim]]], PrimeQ[# + 2] &]2+2;pp=Join[{1}, Select[Range[Lim], GCD@@FactorInteger[#][[All, 2]]>1&]] ;s={};Do[ If[MemberQ[ pp,ts[[n]]],AppendTo[s,ts[[n]]]] ,{n,Length[ts]}];s (* James C. McMahon, Sep 18 2024 *)
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a(N) = for(n=1,N,if(ispower(n),if(nextprime(n/2)-precprime(n/2)==2&&precprime(n/2)+nextprime(n/2)==n,print1(n,", ")))) \\ vary the program's range for any N; Derek Orr, Jul 27 2014
A370453
Twin prime pair sums that equal a twin prime pair product plus 1 (divided by 36).
Original entry on oeis.org
36, 144, 1764, 5184, 360000, 412164, 777924, 4536900, 5673924, 7225344, 12659364, 12830724, 20684304, 37601424, 56972304, 64160100, 81757764, 179506404, 194100624, 255104784, 309689604, 366339600, 461906064, 689062500, 689692644, 1191078144, 1495368900, 1538835984
Offset: 1
144 is a term because 71+73 = 144 and 11*13 = 143.
5184 is a term because 2591+2593 = 5184 and 71*73 = 5183.
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With[{p = Select[Prime[Range[4200]], PrimeQ[# + 2] &]}, Select[p*(p + 2) + 1, And @@ PrimeQ[#/2 + {-1, 1}] &]] (* Amiram Eldar, Feb 19 2024 *)
Showing 1-4 of 4 results.
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