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.

User: Gerard Schildberger

Gerard Schildberger's wiki page.

Gerard Schildberger has authored 4 sequences.

A094480 Unhappy primes, primes that are also unhappy numbers.

Original entry on oeis.org

2, 3, 5, 11, 17, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 107, 113, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 269, 271, 277, 281, 283, 307, 311, 317, 337, 347, 349, 353, 359, 373, 389
Offset: 1

Views

Author

Gerard Schildberger, Jun 05 2004

Keywords

Crossrefs

Cf. unhappy numbers (A031177), happy primes (A035497).

A094343 List of pairs of primes (p, q) with q - p = 4.

Original entry on oeis.org

3, 7, 7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 79, 83, 97, 101, 103, 107, 109, 113, 127, 131, 163, 167, 193, 197, 223, 227, 229, 233, 277, 281, 307, 311, 313, 317, 349, 353, 379, 383, 397, 401, 439, 443, 457, 461, 463, 467, 487, 491, 499, 503, 613, 617, 643
Offset: 1

Views

Author

Gerard Schildberger, Jun 04 2004

Keywords

Comments

The two primes p and p+4 are not necessarily consecutive primes (for that, see A111980).
The pairs are listed in order, sorted by their smallest member. - N. J. A. Sloane, Dec 27 2019

Examples

			The pairs are (3,7), (7,11), (13,17), etc.

Links

Crossrefs

Almost identical to A111980.
Union of A023200 and A046132.
Cf. twin primes (A001097).
See also A000040, A111981, A001097.
For a gap of 6 (which initially is very common) see A140546.

Programs

  • Mathematica
    Flatten[{#,#+4}&/@Select[Prime[Range[200]],PrimeQ[#+4]&]] (* Harvey P. Dale, Apr 13 2011 *)
  • PARI
    isok(n) = (isprime(n) && isprime(n+4)) || (isprime(n-4) && isprime(n)); \\ Michel Marcus, Aug 26 2013

Formula

a(2*n-1)=A023200(n). a(2*n)=A046132(n).

Extensions

Description was corrupted up during editing; correct description restored Aug 21 2005.
a(3) = 7 added by Vincenzo Librandi, May 06 2016

A060365 Multiples of one thousand which are described by single words in American English.

Original entry on oeis.org

1000, 1000000, 1000000000, 1000000000000, 1000000000000000, 1000000000000000000, 1000000000000000000000, 1000000000000000000000000, 1000000000000000000000000000, 1000000000000000000000000000000
Offset: 1

Views

Author

Gerard Schildberger

Keywords

Comments

"Multiples" would include 10000 ("myriad"), 10^100 ("googol"), 10^(10^100) ("googolplex") and maybe 100000 ("lakh") and 10000000 ("crore"). None of these are powers of 1000 (as in the companion sequence A060366). - Robert Dawson, Mar 28 2020

Examples

			10^3 = thousand, 10^6 = million, 10^9 = billion, 10^12 = trillion, 10^15 = quadrillion, etc.

Links

Crossrefs

Cf. A060366.

Programs

Formula

a(n) = 10^(n*3).

A060366 Powers of one thousand which are described by single words in dated British English usage, extended by using "-ard" beyond 10^9.

Original entry on oeis.org

1, 1000, 1000000, 1000000000, 1000000000000, 1000000000000000, 1000000000000000000, 1000000000000000000000, 1000000000000000000000000, 1000000000000000000000000000, 1000000000000000000000000000000
Offset: 1

Views

Author

Gerard Schildberger

Keywords

Examples

			10^0 = one, 10^3 = thousand, 10^6 = million, 10^9 = milliard, 10^12 = billion, etc.

References

  • John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 14.

Links

Crossrefs

Cf. A060365.

Programs

Formula

a(n) = 10^(3*(n-1)).

Extensions

Description changed by Ivan Panchenko, Nov 10 2019

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

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