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.

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

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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

A136582 Sqrt(10)-primes: primes obtained by concatenating the first digits in the decimal expansion of sqrt(10).

Original entry on oeis.org

3, 31, 3162277, 316227766016837933, 316227766016837933199889354443271
Offset: 1

Views

Author

Lekraj Beedassy, Jan 09 2008

Keywords

Comments

n such that floor(sqrt(10^(2*n-1))) is prime (1, 2, 7, 18, 33, ...) are given in A136583.
This sequence is the list of prime terms in A017934.
The next term has 206 digits. - Harvey P. Dale, Dec 06 2023

Crossrefs

Cf. A010467, A017934, A017934, A131581, A132153, A136583, A175733, A175734.

Programs

  • Magma
    // by Jason Kimberley, Aug 2011
for n in [1..499 by 2] do
  f := Isqrt(10^n);
  if IsPrime(f) then
    printf "%o,", f;
  end if;
end for;
  • Mathematica
    Module[{nn=50,sq10},sq10=RealDigits[Sqrt[10],10,nn][[1]];Select[FromDigits/@Table[Take[sq10,n],{n,nn}],PrimeQ]] (* Harvey P. Dale, Dec 06 2023 *)

Formula

a(n) = A017934(2*A136583(n)-1).

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 1-3 of 3 results.

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

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