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.

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A202116 Numbers n such that 90n + 89 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 13, 15, 17, 18, 20, 21, 22, 25, 28, 29, 30, 31, 32, 36, 41, 44, 45, 46, 48, 51, 55, 58, 59, 62, 64, 65, 66, 69, 70, 72, 73, 77, 78, 83, 84, 86, 87, 88, 92, 97, 99, 105, 106, 107, 111, 112, 113, 116, 118, 119, 120, 121, 122, 123, 127, 129
Offset: 1

Views

Author

J. W. Helkenberg, Dec 11 2011

Keywords

Comments

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG?]. Looking at the format 90n+89 modulo 9 and modulo 10 we see that all entries of A142335 have digital root 8 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the PERL program) from the base p,q pairs 89*91, 19*71, 37*17, 73*53, 11*49, 29*31, 47*67, 83*13, 23*43, 41*79, 59*61, 77*7.

Crossrefs

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114, A202115.

Programs

  • Mathematica
    Select[Range[0, 200], PrimeQ[90 # + 89] &]
  • PARI
    is(n)=isprime(90*n+89) \\ Charles R Greathouse IV, Jun 06 2017

A046804 a(n) = p mod (p mod 10) where p = prime(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 3, 1, 2, 2, 0, 2, 0, 1, 5, 2, 5, 0, 4, 0, 1, 7, 2, 8, 6, 0, 1, 2, 1, 2, 1, 0, 4, 4, 5, 0, 3, 1, 6, 2, 8, 0, 0, 1, 1, 1, 0, 1, 3, 4, 2, 5, 0, 0, 5, 2, 8, 0, 4, 0, 1, 2, 6, 0, 1, 2, 0, 1, 4, 7, 2, 8, 3, 1, 1, 2, 2, 5, 0, 4, 5, 0, 0, 1, 7, 2, 8, 2, 0, 1, 5, 2, 4, 0, 4, 2, 5, 0, 1, 0, 1, 4, 2, 2, 0
Offset: 1

Views

Author

Enoch Haga

Keywords

Comments

From Robert G. Wilson v, Feb 12 2014: (Start)
a(n)=0 iff p ends in 1 (A030430) or is a single-digit prime, i.e., 2, 3, 5 or 7 (n = 1, 2, 3 or 4),
a(n)=3 iff n is in A142087,
a(n)=6 iff n is in A142094,
a(n)=7 iff n is in A142330,
a(n)=8 iff n is in A142335.
a(n) can never be 9. (End)

Examples

			prime(10) = 29, so a(10) = 29 mod 9 = 2.

References

  • Idea derived from "The Creation of New Mathematics: An Application of the Lakatos Heuristic," pp. 292-298 of Philip J. Davis and Reuben Hersh, The Mathematical Experience, Houghton Mifflin Co, 1982. ISBN 0-395-32131-X.

Links

Programs

  • Mathematica
    Mod[#,Last[IntegerDigits[#]]]&/@Prime[Range[110]] (* Harvey P. Dale, Jan 23 2013 *)
Mod[#,Mod[#,10]]&/@Prime[Range[110]] (* Harvey P. Dale, Aug 22 2020 *)

Extensions

Name edited by Jon E. Schoenfield, Jan 19 2023
Showing 1-2 of 2 results.

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

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