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Search: id:A119767
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| A119767 |
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Powers that are the sum of twin primes. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Since twin primes greater than (3,5) are either occur as (5,7) mod 12 or (11,1) mod 12, all sums of such twin primes are divisible by 12. Thus all powers are divisible by 12 and are best looked at in base 12. For example, a(2)=5E+61=100, where E is eleven.
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FORMULA
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a(n) = sum twin(n) where twin(n) is the n-th twin prime pair whose sum is a power.
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EXAMPLE
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a(2)=71+73=144.
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MAPLE
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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]<b[1]); map(z->z[3], L);
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CROSSREFS
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Sequence in context: A044749 A067865 A049227 this_sequence A016910 A005017 A110754
Adjacent sequences: A119764 A119765 A119766 this_sequence A119768 A119769 A119770
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KEYWORD
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easy,nonn
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AUTHOR
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Walter Kehowski (wkehowski(AT)cox.net), Jun 18 2006
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