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Search: id:A119768
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| A119768 |
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Twin prime pairs that sum to a power. |
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+0
1
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| 17, 19, 71, 73, 107, 109, 881, 883, 1151, 1153, 2591, 2593, 3527, 3529, 4049, 4051, 15137, 15139, 20807, 20809, 34847, 34849, 46817, 46819, 69191, 69193, 83231, 83233, 103967, 103969, 112337, 112339, 139967, 139969, 149057, 149059, 176417
(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 prime pairs greater than (3,5) occur as either (5,7) mod 12 or (11,1) mod 12, all sums of such twin primes are always divisible by 12. Thus all powers are divisible by 12. The first few terms in base 12 are: 15, 17, 5E, 61, 8E, 91, 615, 617, 7EE, 801, 15EE, 1601 and the corresponding powers are 30, 100, 160, 1030, 1400, 3000.
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FORMULA
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If a(n) is the above sequence of twin primes, then a(2n-1),a(2n) is a twin prime pair and a(2n-1)+a(2n) is a power.
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EXAMPLE
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a(3)+a(4)=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->op(z[1..2]), L);
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CROSSREFS
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Sequence in context: A144709 A132239 A075432 this_sequence A005808 A028489 A165320
Adjacent sequences: A119765 A119766 A119767 this_sequence A119769 A119770 A119771
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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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