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).

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

Offset: 1

Author

Chai Wah Wu, May 09 2015

Keywords

• nonn

Comments

Similar to A257582, but converging to e.

Examples

			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...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000
• 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.

Crossrefs

Cf. A001113 (e), A257582 (analog for Pi instead of e), A257809 (analog for delta = 4.6692...), A257574.

Programs

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

Extensions

Edited by M. F. Hasler, May 03 2018