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.

A241947 Numbers n for which A241927(n) = 2.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 20
Offset: 1

Views

Author

Vladimir Shevelev, May 03 2014

Keywords

Comments

If the sequence contains no perfect squares>4, then the Goldbach conjecture in Fermi-Dirac arithmetic (FDGC) is true (see comment in A241927).
Essentially, the sequence is the Fermi-Dirac analog of A100570. Since A100570 is conjecturally finite, it is natural to suppose that this sequence is also finite.
There is not another term up to 10^6. - Peter J. C. Moses, May 05 2014
Thus, if 20 is the last term of the sequence, then the FDGC is true. - Vladimir Shevelev, May 05 2014

Crossrefs

Cf. A241927, A241922, A100570.

Extensions

Name corrected by Michel Marcus, Dec 14 2018

A217742 Numbers n with the property that if the base-8 representation of n is read backwards, the result is 5*n.

Original entry on oeis.org

525, 4725, 34125, 38325, 269325, 307125, 2150925, 2184525, 2423925, 2457525, 17203725, 17506125, 19358325, 19660725, 137626125, 137894925, 139810125, 140078925, 154833525, 155102325, 157017525, 157286325
Offset: 1

Views

Author

N. J. A. Sloane, Mar 23 2013

Keywords

Examples

			n = 525 (base 10) = 1015 (base 8). Reading this backwards we get 5101 (base 8) = 2625 (base 10) = 5*n, so 525 is in the sequence.

Crossrefs

Cf. A241927, A223089.

A242165 Smallest k>=0, such that n+/-k are both Fermi-Dirac primes (A050376).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 0, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 4, 3, 6, 5, 0, 9, 2, 3, 0, 1, 0, 3, 2, 3, 0, 1, 0, 3, 2, 9, 0, 5, 6, 3, 4, 9, 0, 1, 0, 9, 4, 3, 6, 5, 0, 15, 2, 3, 0, 1, 0, 7, 4, 3, 4, 5, 0, 1, 0, 1, 0, 5, 4, 3, 14, 9, 0, 7, 10, 9, 4, 13, 6, 7, 0
Offset: 2

Views

Author

Vladimir Shevelev, May 05 2014

Keywords

Comments

The existence of a(n)>=0 for all n >= 2 is equivalent to the Goldbach conjecture in Fermi-Dirac arithmetic (cf. comment in A241927) that every even number >= 4 is a sum of two terms of A050376 (it is slightly weaker than Goldbach conjecture for primes).

References

  • V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 (in Russian; MR 2000f: 11097, pp. 3912-3913).

Links

Crossrefs

Cf. A082467, A241922, A241927, A241947.

Formula

a(A050376(n)) = 0.
Showing 1-3 of 3 results.

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

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