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A257764 Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces the decimal expansion of e (Euler's number).

%I A257764 #13 May 04 2018 11:26:35
%S A257764 3,13,31,59,67,103,179,193,227,229,317,983,1201,1213,1321,1787,1811,
%T A257764 2179,3571,4817,5333,6803,10433,12197,13063,19391,21283,24571,31817,
%U A257764 42307,45377,49957,61909,67933,70573,74843,82421,85909,91099,99241,101293,109639,112087
%N A257764 Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces the decimal expansion of e (Euler's number).
%C A257764 Similar to A257582, but converging to e.
%H A257764 Chai Wah Wu, <a href="/A257764/b257764.txt">Table of n, a(n) for n = 1..1000</a>
%H A257764 Popular Computing (Calabasas, CA), <a href="/A257352/a257352.pdf">The CSR Function</a>, Vol. 4 (No. 34, Jan 1976), pages PC34-10 to PC34-11. Annotated and scanned copy.
%H A257764 Herman P. Robinson, <a href="/A257574/a257574.pdf">The CSR Function</a>, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.
%e A257764 sqrt(3) =  1.7320508075688772...
%e A257764 sqrt(3+sqrt(13)) = 2.570126704165378...
%e A257764 sqrt(3+sqrt(13+sqrt(31))) = 2.703522309917472...
%e A257764 sqrt(3+sqrt(13+sqrt(31+sqrt(59)))) = 2.7173508299457327...
%e A257764 sqrt(3+sqrt(13+sqrt(31+sqrt(59+sqrt(67))))) = 2.718217091497069...
%e A257764 sqrt(3+sqrt(13+sqrt(31+sqrt(59+sqrt(67+sqrt(103)))))) = 2.7182780002752187...
%o A257764 (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
%Y A257764 Cf. A001113 (e), A257582 (analog for Pi instead of e), A257809 (analog for delta = 4.6692...), A257574.
%K A257764 nonn
%O A257764 1,1
%A A257764 _Chai Wah Wu_, May 09 2015
%E A257764 Edited by _M. F. Hasler_, May 03 2018