A257582 - OEIS

%I #26 May 05 2018 17:53:52

%S 5,17,37,53,131,181,263,317,859,887,1637,2837,3413,5861,6491,10531,

%T 13399,14083,14563,21433,29717,30529,31663,31771,32069,32587,36559,

%U 36809,39359,39461,45319,46933,49801,52391,52579,52889,55871,57493,59107,59539,64187,64633,75377,77491,82351,86587

%N Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces Pi.

%C The continued square root map applied to a sequence (x,y,z,...) is CSR(x,y,z,...) = sqrt(x + sqrt(y + sqrt(z + ...))); this is well defined if the logarithm of the terms is O(2^n).

%H Chai Wah Wu, <a href="/A257582/b257582.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 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.

%o (PARI) (CSR(v, s)=forstep(i=#v, 1, -1, s=sqrt(v[i]+s)); s); a=[5]; for(n=1, 50, print1(a[#a]", "); for(i=primepi(a[#a])+1, oo, CSR(concat(a, vector(9, j, prime(i+j))))>=Pi && (a=concat(a, prime(i))) && break)) \\ The default precision of 38 digits yields correct terms only below 30000. To compute larger values correctly, realprecision must be increased. - _M. F. Hasler_, May 03 2018

%Y Cf. A000796 (Pi), A257764 (analog for e = 2.71828... instead of Pi), A257809 (analog for delta = 4.6692...), A257574.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, May 03 2015

%E a(15)-a(46) from _Chai Wah Wu_, May 06 2015

%E Edited by _M. F. Hasler_, May 03 2018