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 1-2 of 2 results.

A239478 Integer solutions of the arithmetic differential equation m' = m + sqrt(m).

Original entry on oeis.org

225, 184041, 741321, 1095543801
Offset: 1

Views

Author

Paolo P. Lava, Mar 20 2014

Keywords

Comments

a(5) > 10^17. - Giovanni Resta, Mar 20 2014
m = k^2, where k satisfies k' = (k+1)/2. - Charlie Neder, Mar 08 2019

Examples

			For m = 225 we have that m' = 240, sqrt(225) = 15 and 240 = 225 + 15.

Crossrefs

Cf. A003415, A239479.

Programs

  • Maple
    with(numtheory); P:= proc(q) local n,p,x;
for n from 1 to q do x:=n^2;
if x*add(op(2,p)/op(1,p),p=ifactors(x)[2])=n^2+n then print(n^2);
fi; od; end: P(10^9);

A287102 Numbers k such that (10^(4*k+1)*37 + 10^(2*k)*(-99) - 73)/99 is prime (k > 0).

Original entry on oeis.org

1, 9, 441, 2980
Offset: 1

Views

Author

Mikk Heidemaa, May 19 2017

Keywords

Comments

Or '37'||...'37'||'2'||'73'...||'73' in decimal form is prime (as a string, it consists of a middle '2' with the prefix composed of '37' concatenated k times, and the suffix composed of '73' concatenated k times).
a(5), if it exists, is greater than 58079. - Robert Price, May 03 2018

Examples

			9 is a term because (10^(4*9+1)*37 + 10^(2*9)*(-99) - 73)/99 = 3737373737373737372737373737373737373 (prime). As a string, it consists of a middle '2' with the prefix '373737373737373737' ('37' concatenated 9 times) and the suffix '737373737373737373' ('73' concatenated 9 times).

Crossrefs

Cf. A173954, A239479.

Programs

  • Mathematica
    ParallelMap[ If[ PrimeQ[ (10^(4*#+1)*37+10^(2*#)*(-99)-73)/99], #, Nothing]&, Range[3000]]
Showing 1-2 of 2 results.

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

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