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 1-4 of 4 results.

A060421 Numbers k such that the first k digits of the decimal expansion of Pi form a prime.

Original entry on oeis.org

1, 2, 6, 38, 16208, 47577, 78073, 613373
Offset: 1

Views

Author

Michel ten Voorde, Apr 05 2001

Keywords

Comments

The Brown link states that in 2001 Ed T. Prothro reported discovering that 16208 gives a probable prime and that Prothro verified that all values for 500 through 16207 digits of Pi are composites. - Rick L. Shepherd, Sep 10 2002
The corresponding primes are in A005042. - Alexander R. Povolotsky, Dec 17 2007

Examples

			3 is prime, so a(1) = 1; 31 is prime, so a(2) = 2; 314159 is prime, so a(3) = 6; ...

Links

Crossrefs

Cf. A000796 (Pi), A005042, A007523, A047658.
Primes in other constants: A064118 (e), A065815 (gamma), A064119 (phi), A118328 (Catalan's constant), A115377 (sqrt(2)), A119344 (sqrt(3)), A228226 (log 2), A228240 (log 10), A119334 (zeta(3)), A122422 (Soldner's constant), A118420 (Glaisher-Kinkelin constant), A174974 (Golomb-Dickman constant), A118327 (Khinchin's constant).
In other bases: A065987 (binary), A065989 (ternary), A065991 (quaternary), A065990 (quinary), A065993 (senary).

Programs

  • Mathematica
    Do[If[PrimeQ[FromDigits[RealDigits[N[Pi, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 9016} ]

Extensions

a(6) = 47577 from Eric W. Weisstein, Apr 01 2006
a(7) = 78073 from Eric W. Weisstein, Jul 13 2006
a(8) = 613373 from Adrian Bondrescu, May 29 2016

A064118 Numbers k such that the first k digits of e form a prime.

Original entry on oeis.org

1, 3, 7, 85, 1781, 2780, 112280, 155025
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 09 2001

Keywords

Comments

The primes are given in A007512. Sequences A065815, A119344, A136583, A210706,... are analogs for gamma, sqrt(3), sqrt(10), 3^(1/3), .... The MathWorld page about "Constant Primes" lists further examples. - M. F. Hasler, Aug 31 2013

Examples

			a(2)=3 because the 3-digit number 271 is prime.

References

  • C. A. Pickover, The Mathematics of Oz, "2, 271, 2718281", Chapter 95, Camb.Univ.Press, UK 2002.

Links

Crossrefs

Cf. A001113.
Cf. A047658.

Programs

  • Mathematica
    Do[If[PrimeQ[FromDigits[RealDigits[N[E, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 2300}]

Extensions

One more term from Robert G. Wilson v, Sep 28 2001
a(6) from Eric W. Weisstein, Jan 17 2005
a(7) from Eric W. Weisstein, Jul 03 2009
a(8) from Eric W. Weisstein, Oct 11 2010

A119343 Theodorus primes: primes formed from the concatenation of the initial decimal digits of Theodorus's constant, sqrt(3).

Original entry on oeis.org

17, 173, 1732050807568877293
Offset: 1

Views

Author

Eric W. Weisstein, May 15 2006

Keywords

Comments

The next term (a(4)) has 111 digits. - Harvey P. Dale, Oct 24 2014

Examples

			sqrt(3) = 1.732050807568877..., 17, the concatenation of the first 2 decimal digits, is prime, so a(1) = 17.

Links

Crossrefs

Cf. A002194, A119344.

Programs

  • Mathematica
    nn=300;With[{ds3=RealDigits[Sqrt[3],10,nn][[1]]},Select[ Table[ FromDigits[ Take[ds3,n]],{n,nn}],PrimeQ]] (* Harvey P. Dale, Oct 24 2014 *)

Extensions

Edited by Charles R Greathouse IV, Apr 27 2010

A210706 Numbers k such that floor[ 3^(1/3)*10^k ] is prime.

Original entry on oeis.org

23, 80, 2487
Offset: 1

Views

Author

M. F. Hasler, Aug 31 2013

Keywords

Comments

Inspired by prime curios about 4957 (cf. LINKS), one of which honors the late Bruce Murray (Nov 30 1931 - Aug 29 2013).
Meant to be a "condensed" version of A210704, see there for more.
Alternate definition: Numbers k such that concatenation of the first (k+1) digits of A002581 yields a prime.

Examples

			t = 3^(1/3) = 1.44224957030740838232163831... multiplied by 10^23 yields
t*10^23 = 144224957030740838232163.831..., the integer part of which is the prime A210704(1), therefore a(1)=23.

Links

Crossrefs

Cf. A002581 = decimal expansion of 3^(1/3).
Cf. A065815 (analog for gamma), A060421 (1+ analog for Pi), A064118 (1+ analog for exp(1)), A119344 (1 + analog for sqrt(3)), A136583 (1+ analog for sqrt(10)).

Programs

  • PARI
    \p2999
t=sqrtn(3,3);for(i=1,2999,ispseudoprime(t\.1^i)&print1(i","))

Formula

a(n) = (length of A210704(n)) - 1, where "length" means number of decimal digits.
Showing 1-4 of 4 results.

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