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A257764
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Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces the decimal expansion of e (Euler's number).
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4
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3, 13, 31, 59, 67, 103, 179, 193, 227, 229, 317, 983, 1201, 1213, 1321, 1787, 1811, 2179, 3571, 4817, 5333, 6803, 10433, 12197, 13063, 19391, 21283, 24571, 31817, 42307, 45377, 49957, 61909, 67933, 70573, 74843, 82421, 85909, 91099, 99241, 101293, 109639, 112087
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OFFSET
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1,1
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COMMENTS
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Similar to A257582, but converging to e.
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LINKS
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Popular Computing (Calabasas, CA), The CSR Function, Vol. 4 (No. 34, Jan 1976), pages PC34-10 to PC34-11. Annotated and scanned copy.
Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.
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EXAMPLE
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sqrt(3) = 1.7320508075688772...
sqrt(3+sqrt(13)) = 2.570126704165378...
sqrt(3+sqrt(13+sqrt(31))) = 2.703522309917472...
sqrt(3+sqrt(13+sqrt(31+sqrt(59)))) = 2.7173508299457327...
sqrt(3+sqrt(13+sqrt(31+sqrt(59+sqrt(67))))) = 2.718217091497069...
sqrt(3+sqrt(13+sqrt(31+sqrt(59+sqrt(67+sqrt(103)))))) = 2.7182780002752187...
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PROG
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(PARI) (CSR(v, s)=forstep(i=#v, 1, -1, s=sqrt(v[i]+s)); s); a=[3]; for(n=1, 50, print1(a[#a]", "); for(i=primepi(a[#a])+1, oo, CSR(concat(a, vector(9, j, prime(i+j))))>=exp(1)&& (a=concat(a, prime(i)))&& break)) \\ The standard precision of 38 digits yields incorrect terms beyond 10433. Increase realprecision to compute larger values. - M. F. Hasler, May 03 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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