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.

A135584 Duplicate of A124013.

Original entry on oeis.org

3, 3, 3, 59, 11, 17, 29, 11, 71, 71, 23, 11, 29, 29, 11, 83, 3, 11, 281, 11, 101, 71, 23, 257, 401, 293, 107, 293, 53, 11, 113, 251, 47, 587, 23, 179, 389, 59, 173, 17, 1427, 83, 431, 53, 563, 593, 41, 47, 239, 383, 431, 1181, 701, 971, 149, 593, 569, 149, 191, 1973
Offset: 1

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Author

Keywords

A124450 Lesser of a pair of not necessarily distinct closest primes that add up to 10^n.

Original entry on oeis.org

5, 47, 491, 4919, 49877, 499943, 4999913, 49999757, 499999931, 4999999937, 49999999811, 499999999769, 4999999998431, 49999999999619, 499999999999769, 4999999999998557, 49999999999998887, 499999999999999679, 4999999999999999661, 49999999999999998647
Offset: 1

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Author

Zak Seidov, Nov 02 2006

Keywords

Comments

a(n) is always an n digit number.
Note that if distinct primes are required, the only change is that a(1) = 3.

Examples

			10^1=5+5; 10^2=47+53; 10^3=491+509;
10^4=4919+5081; 10^5=49877=50123; 10^6=499943+500057;
10^7=4999913+5000087; 10^8=49999757+50000243;
10^9=499999931+500000069;
10^10=4999999937+5000000063; etc.

Links

Crossrefs

Cf. A065577 (number of Goldbach partitions of 10^n).
Cf. A124013.

Programs

  • Mathematica
    Table[ h =10^n/2; c=0; While[ PrimeQ[ h-c ]==False || PrimeQ[ h+c ]==False, c++ ]; h-c, {n, 1, 50} ] (* Hans Havermann, Nov 02 2006 *)

Formula

10^n - a(n) is prime.

Extensions

Edited by N. J. A. Sloane May 15 2008 at the suggestion of R. J. Mathar.

A124049 a(n) = c is least number such that 10^n/2 -/+ c are primes.

Original entry on oeis.org

0, 3, 9, 81, 123, 57, 87, 243, 69, 63, 189, 231, 1569, 381, 231, 1443, 1113, 321, 339, 1353, 363, 519, 1323, 1503, 741, 1221, 957, 1053, 339, 5931, 2121, 2301, 2031, 4773, 4737, 10281, 1317, 129, 3873, 1443, 387, 11769, 8271, 5337, 2883, 7137, 8193, 8493
Offset: 1

Views

Author

Hans Havermann and Zak Seidov, Nov 03 2006

Keywords

Comments

Related to Goldbach pairs of 10^n: a(n)=10^n/2 -A124450(n) Lesser of pair of closest primes whose sum is 10^n. Cf. A124013 Lesser of pair of most widely separated primes whose sum is 10^n, A065577 Number of Goldbach partitions of 10^n
All terms are divisible by 3 - see A108163.

Examples

			Next terms up to n = 101: 14637, 9897,
6471, 183, 8043, 6921,6699, 29127, 3663, 12537, 3777,
6741, 2253, 561, 3783, 26979, 16491, 6543, 10683,
1749, 6417, 38871, 22767, 62403, 8631, 4497, 20739,
453, 16731, 25293, 4341, 37467,
55323,4587,37083,24717,6687,8763,22551,29367,37881,14301,8637,34101,22179,26811,7059,1647

Crossrefs

Cf. A065577, A124013, A124450.

Programs

  • Mathematica
    lnc[n_]:=Module[{c=0,t=10^n/2},While[!AllTrue[t+{c,-c},PrimeQ],c++];c]; Array[ lnc,50] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 21 2014 *)
Showing 1-3 of 3 results.

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

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