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.

A288021 Prime p1 of consecutive primes p1, p2, where p2 - p1 = 4, and p1, p2 are in different decades.

Original entry on oeis.org

7, 19, 37, 67, 79, 97, 109, 127, 229, 277, 307, 349, 379, 397, 439, 457, 487, 499, 739, 757, 769, 859, 877, 907, 937, 967, 1009, 1087, 1279, 1297, 1429, 1447, 1489, 1549, 1567, 1579, 1597, 1609, 1867, 1999, 2137, 2239, 2269, 2347, 2377, 2389, 2437, 2539, 2617, 2659, 2689, 2707, 2749, 2797, 2857
Offset: 1

Views

Author

Hartmut F. W. Hoft, Jun 04 2017

Keywords

Comments

The unit digits of the numbers in the sequence are 7's or 9's.

Examples

			7 is in this sequence since pair (7,11) is the first with difference 4 spanning a multiple of 10.

Crossrefs

Cf. A001359, A023201, A023203, A031924, A031925, A031928, A046117, A046132, A158277, A158861, A160370, A160440, A160500, A287049, A287050, A060229, A288022, A288024.

Programs

  • Mathematica
    a288021[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[10, n, 10]], First[#]-Last[#]==4&]]
a288021[3000] (* data *)

A288022 Prime p1 of consecutive primes p1, p2, where p2 - p1 = 6, and p1, p2 are in different decades.

Original entry on oeis.org

47, 157, 167, 257, 367, 557, 587, 607, 647, 677, 727, 947, 977, 1097, 1117, 1187, 1217, 1367, 1657, 1747, 1777, 1907, 1987, 2207, 2287, 2417, 2467, 2677, 2837, 2897, 2957, 3307, 3407, 3607, 3617, 3637, 3727, 3797, 4007, 4357, 4457, 4507, 4597, 4657, 4937, 4987
Offset: 1

Views

Author

Hartmut F. W. Hoft, Jun 04 2017

Keywords

Comments

The unit digits of the numbers in the sequence are 7's.
Number of terms < 10^k: 0, 0, 1, 13, 81, 565, 4027, 30422, 237715, ... - Muniru A Asiru, Jan 09 2018

Examples

			47 is in the sequence since pair (47,53) is the first with difference 6 spanning a multiple of 10.

Links

Crossrefs

Cf. A001359, A023201, A023203, A031924, A031925, A031928, A046117, A046132, A158277, A158861, A160370, A160440, A160500, A287049, A287050, A060229, A288021, A288024.

Programs

  • GAP
    P:=Filtered([1..20000], IsPrime);
P1:=List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=6),j->j[1] mod 5=2),k->k[1]); # Muniru A Asiru, Jul 08 2017
  • Maple
    for n from 1 to 2000 do if [ithprime(n+1)-ithprime(n), ithprime(n) mod 5] = [6,2] then print(ithprime(n)); fi; od; # Muniru A Asiru, Jan 19 2018
  • Mathematica
    a288022[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[10, n, 10]], First[#]-Last[#]==6&]]
a288022[3000] (* data *)

A288024 Prime p1 of consecutive primes p1, p2, where p2 - p1 = 8, and p1, p2 are in different decades.

Original entry on oeis.org

89, 359, 389, 449, 479, 683, 719, 743, 929, 983, 1109, 1163, 1193, 1373, 1439, 1523, 1559, 1733, 1823, 1979, 2003, 2153, 2213, 2243, 2273, 2459, 2609, 2663, 2699, 2843, 2879, 2909, 3209, 3449, 3623, 3719, 4289, 4349, 4583, 4943, 5189, 5399, 5573, 5693, 5783, 5813
Offset: 1

Views

Author

Hartmut F. W. Hoft, Jun 04 2017

Keywords

Comments

The unit digits of the numbers in the sequence are 3's or 9's.

Examples

			89 is in the sequence since pair (89,97) is the first with difference 8 spanning a multiple of 10.

Links

Crossrefs

Cf. A001359, A023201, A023203, A031924, A031925, A031928, A046117, A046132, A158277, A158861, A160370, A160440, A160500, A287049, A287050, A060229, A288021, A288022.

Programs

  • Mathematica
    a288024[n_] := Map[Last, Select[Map[{NextPrime[#, 1], NextPrime[#, -1]}&, Range[10, n, 10]], First[#]-Last[#]==8&]]
a288024[6000] (* data *)
Select[Partition[Prime[Range[800]],2,1],#[[2]]-#[[1]]==8&&IntegerDigits[#[[1]]][[-2]]!= IntegerDigits[ #[[2]]][[-2]]&][[;;,1]] (* Harvey P. Dale, Jan 09 2024 *)
Showing 1-3 of 3 results.

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