A257582 Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces Pi.

5, 17, 37, 53, 131, 181, 263, 317, 859, 887, 1637, 2837, 3413, 5861, 6491, 10531, 13399, 14083, 14563, 21433, 29717, 30529, 31663, 31771, 32069, 32587, 36559, 36809, 39359, 39461, 45319, 46933, 49801, 52391, 52579, 52889, 55871, 57493, 59107, 59539, 64187, 64633, 75377, 77491, 82351, 86587

Offset

1,1

Comments

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).

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.

Prog

(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

Crossrefs

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

Sequence in context: A060245 A119456 A264904 * A339988 A273538 A273212

Adjacent sequences: A257579 A257580 A257581 * A257583 A257584 A257585

Keyword

nonn

Author

N. J. A. Sloane, May 03 2015

Extensions

a(15)-a(46) from Chai Wah Wu, May 06 2015

Edited by M. F. Hasler, May 03 2018

Status

approved