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A257582
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Lexicographically largest increasing sequence of primes for which the continued square root map (see A257574) produces Pi.
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4
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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