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.

A007512 Primes of the form floor(e*10^k), i.e., formed by concatenation of an initial segment of the decimal expansion of e.

Original entry on oeis.org

2, 271, 2718281, 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571
Offset: 1

Views

Author

N. J. A. Sloane, Robert G. Wilson v, Simon Plouffe

Keywords

Comments

The number of digits in a(n) is given in A064118. This allows us to get larger terms that cannot be displayed here, via the given FORMULA. Sequences A005042, A072952, A115453, A119343, A210704, ... are the analogs for Pi, gamma, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Programs

  • Maple
    Digits := 110; n0 := evalf(E); for i from 1 to 100 do t1 := trunc(10^i*n0); if isprime(t1) then print(t1); fi; od:
  • PARI
    c=exp(1);for(k=0,precision(c),ispseudoprime(c\.1^k) & print1(c\.1^k,",")) \\ M. F. Hasler, Sep 01 2013

Formula

a(n) = floor(e*10^(A064118(n)-1)). - M. F. Hasler, Aug 31 2013

Extensions

Next term is a 1781-digit BPSW-probable prime 2718281828459045235...211151368350627526023. - Randall L Rathbun, Feb 02 2002
Edited by T. D. Noe, Oct 30 2008
Edited by M. F. Hasler, Aug 31 2013

A210704 Primes formed by initial digits of 3^(1/3) = A002581, i.e., of the form floor[3^(1/3)*10^k].

Original entry on oeis.org

144224957030740838232163, 144224957030740838232163831078010958839186925349935057754641619454168759682999733
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, 30.11.1931 - 29.8.2013.
See A210706 for the k-values. The keyword "less" for this records means that the next term (2488 digits) cannot be added / displayed here, and instead of listing further primes here, the k-values should be recorded in A210706.

Links

Crossrefs

Cf. A005042 (analog for Pi), A007512 (analog for e), A115453 (analog for sqrt(2)), A119343 (analog for sqrt(3)), A072952 (analog for gamma).

Programs

  • Mathematica
    With[{cr3=RealDigits[CubeRoot[3],10,100][[1]]},Select[Table[FromDigits[Take[cr3,n]],{n,100}],PrimeQ]] (* Harvey P. Dale, Mar 30 2024 *)
  • PARI
    (c=sqrtn(3,3),v=1/*set to 0 for indices instead of values*/)->for(k=0,precision(c),ispseudoprime(p=c\.1^k)&&print1([k,p][1+v]","))

Formula

a(n) = floor[A002581 * 10^A210706(n)], where A002581 is taken as a constant.

A242835 Primes formed by the initial digits of the decimal expansion of the square root of 5.

Original entry on oeis.org

2, 223, 22360679774997896964091
Offset: 1

Views

Author

Felix Fröhlich, May 23 2014

Keywords

Comments

There is no other term with less than 111 digits.
a(4) has 1506 digits. - Hiroaki Yamanouchi, Sep 11 2014

Examples

			Decimal expansion of sqrt(5) begins: 2.23606797749978969640917366... - _Wesley Ivan Hurt_, May 26 2014

Crossrefs

Cf. A005042, A007512, A072952, A119343.
Cf. A002163 (Decimal Expansion of sqrt(5)).

Programs

  • Mathematica
    Module[{d=25,f},f=RealDigits[Sqrt[5],10,d][[1]];Select[ Table[ FromDigits[ Take[f,n]],{n,d}],PrimeQ]] (* Harvey P. Dale, Oct 29 2020 *)
Showing 1-3 of 3 results.

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

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