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A132746
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Numbers k such that prime(k) + prime(k+1) is a perfect power.
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0
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2, 7, 15, 18, 20, 28, 61, 152, 190, 293, 377, 492, 558, 564, 789, 919, 942, 1332, 1768, 2343, 2429, 2693, 2952, 3136, 3720, 3928, 4837, 5421, 5722, 6870, 7347, 8126, 8193, 9465, 9857, 9927, 10410, 10483, 10653, 12685, 13005, 13763, 13955, 16033, 16342
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OFFSET
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1,1
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COMMENTS
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First terms absent in A064397: 2, 18, 28, 564, 1332, 3928, 12415, 13005, 16886.
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LINKS
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EXAMPLE
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2 is a term because prime(2) + prime(3) = 3 + 5 = 8 = 2^3 (perfect power);
7 is a term because prime(7) + prime(8) = 17 + 19 = 36 = 6^2 (perfect power);
39867 is a term because prime(39867) + prime(39868) = 478241 + 478243 = 956484 = 978^2 (perfect power).
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PROG
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(PARI) s=[]; for(n=1, 41530, a=prime(n)+prime(n+1); if(ispower(a), s=concat(s, n))); s
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CROSSREFS
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Cf. A064397 (numbers k such that prime(k) + prime(k+1) is a square).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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