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A332203
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a(n) = 2^(2^n-1) + 1.
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1
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2, 3, 9, 129, 32769, 2147483649, 9223372036854775809, 170141183460469231731687303715884105729, 57896044618658097711785492504343953926634992332820282019728792003956564819969
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OFFSET
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0,1
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COMMENTS
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All terms > 2 are divisible by 3. Moreover, the exponent of the highest power of 3 dividing a(n) behaves like a mixture of 2- and 3-adic ruler function, after the initial 0: (1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, ...) = A332202.
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LINKS
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FORMULA
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PROG
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(PARI) apply( {A332203(n)=1<<(1<<n-1)+1}, [0..9])
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CROSSREFS
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Cf. A077585 (Double Mersenne numbers: same with -1), A000225 (Mersenne numbers 2^n-1).
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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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