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A257582 Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces Pi. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A273538 A273212 A273274

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

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Last modified March 31 19:37 EDT 2020. Contains 333151 sequences. (Running on oeis4.)