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 A119768 Twin prime pairs that sum to a power. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS FORMULA 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. EXAMPLE a(3)+a(4)=71+73=144. MAPLE 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]op(z[1..2]), L); CROSSREFS Sequence in context: A132239 A075432 A232882 * A232878 A226681 A005808 Adjacent sequences:  A119765 A119766 A119767 * A119769 A119770 A119771 KEYWORD easy,nonn AUTHOR Walter Kehowski, Jun 18 2006 STATUS approved

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