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A301804
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Sequence satisfies: 1 = Sum_{n>=1} 2^(n*(n-1)) / a(n)^n, with a(1) = 2, by a greedy algorithm.
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1
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2, 3, 11, 28, 67, 181, 540, 1605, 4500, 12770, 37773, 127030, 444950, 1379830, 4396237, 13632772, 45274296, 158468043, 530856473, 1800446217, 6279909810, 24743271334, 85850127322, 290413108775, 977634838108, 3306283825369, 11185652749615, 38838048510711, 133953360029207, 459989927920851, 1634605692726786, 5918370893528999, 20465922530700426, 71980481052561822, 265331221445369542
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OFFSET
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1,1
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COMMENTS
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It appears that the limit a(n+1)/a(n) exists and is near 4.
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LINKS
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EXAMPLE
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1 = 1/2 + 2^2/3^2 + 2^6/11^3 + 2^12/28^4 + 2^20/67^5 + 2^30/181^6 + 2^42/540^7 + 2^56/1605^8 + 2^72/4500^9 + 2^90/12770^10 + 2^110/37773^11 + 2^132/127030^12 + 2^156/444950^13 + 2^182/1379830^14 + 2^210/4396237^15 + 2^240/13632772^16 + 2^272/45274296^17 + 2^306/158468043^18 + 2^342/530856473^19 + 2^380/1800446217^20 + 2^420/6279909810^21 + ... + ( 2^(n-1)/a(n) )^n + ...
Incidentally,
Sum_{n>=1} 2^(n-1)/a(n) = 2.594806011516631787617662898514062588686879234...
Sum_{n>=1} 2^(n^2)/a(n)^n = 3.295922872490926100815120594347157182861242917...
Sum_{n>=1} 2^(n*(n+1))/a(n)^n = 14.82031378016256272989741456078817533736...
Sum_{n>=1} 1/a(n) = 0.983220030675069959469784597542593767565029822764...
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PROG
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(PARI) /* Must have appropriate precision for N terms: */ N = 100;
{A=[2]; for(i=1, N, A=concat(A, 1 + floor((1/(1 - sum(n=1, #A, (2^n)^(n-1)/A[n]^n *1.))*2^((#A)*(#A+1)) )^(1/(#A+1))) ) ; print1(#A, ", ")); A}
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CROSSREFS
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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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