cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, May 03 2015

Keywords

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.

Crossrefs

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

Programs

  • 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

Extensions

a(15)-a(46) from Chai Wah Wu, May 06 2015
Edited by M. F. Hasler, May 03 2018

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).

Original entry on oeis.org

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

Views

Author

Chai Wah Wu, May 09 2015

Keywords

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

A257858 An increasing sequence of integers for which the continued square root map (see A257574) produces the decimal expansion of Pi.

Original entry on oeis.org

6, 10, 19, 27, 29, 32, 42, 45, 56, 67, 75, 94, 109, 122, 138, 144, 151, 152, 172, 181, 194, 204, 205, 232, 256, 290, 316, 325, 346, 380, 412, 446, 478, 511, 520, 533, 580, 584, 617, 623, 654, 658, 661, 682, 734, 773, 823, 836, 865, 903, 954, 979, 997, 1008, 1059
Offset: 1

Views

Author

Chai Wah Wu, May 13 2015

Keywords

Examples

			sqrt(6) = 2.449489742783178
sqrt(6+sqrt(10)) = 3.0269254467476365
sqrt(6+sqrt(10+sqrt(19))) = 3.1287879095060176
sqrt(6+sqrt(10+sqrt(19+sqrt(27)))) = 3.140462825727146
sqrt(6+sqrt(10+sqrt(19+sqrt(27+sqrt(29))))) = 3.1414928066743406

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. A257582, A257764, A257809.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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