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.

Previous Showing 31-34 of 34 results.

A287304 Primes that can be generated by the concatenation in base 5, in ascending order, of two consecutive integers read in base 10.

Original entry on oeis.org

7, 13, 19, 131, 157, 313, 443, 521, 547, 599, 3529, 3907, 4159, 4663, 4789, 5167, 5419, 5923, 6301, 6427, 6553, 6679, 7057, 7309, 7561, 7687, 8191, 8317, 8443, 8821, 9199, 9829, 10333, 10459, 10711, 10837, 11467, 11593, 11719, 11971, 12097, 12601, 12853, 12979
Offset: 1

Views

Author

Paolo P. Lava, May 23 2017

Keywords

Examples

			1 and 2 in base 5 are 1 and 2 and concat(1,2) = 12 in base 10 is 7;
6 and 7 in base 5 are 11 and 12 and concat(11,12) = 1112 in base 10 is 157.

Crossrefs

Cf. A000040, A030458.

Programs

  • Maple
    with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; a:=convert(q+1,base,h); b:=convert(q,base,h); c:=[op(a),op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i,5),i=1..1000);
  • Mathematica
    With[{b = 5}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 120, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)
Select[FromDigits[Flatten[#],5]&/@Partition[IntegerDigits[Range[150],5],2,1],PrimeQ] (* Harvey P. Dale, Nov 25 2020 *)

A287306 Primes that can be generated by the concatenation in base 6, in ascending order, of two consecutive integers read in base 10.

Original entry on oeis.org

29, 223, 593, 1259, 8681, 11719, 14323, 16493, 16927, 18229, 19531, 20399, 21701, 23003, 26041, 28211, 29947, 31249, 32117, 34721, 36457, 39929, 41231, 42533, 42967, 44269, 45137, 46439, 293123, 316469, 324251, 350191, 355379, 363161, 381319, 396883, 402071, 425417
Offset: 1

Views

Author

Paolo P. Lava, May 23 2017

Keywords

Examples

			4 and 5 in base 6 are 4 and 5 and concat(4,5) = 45 in base 10 is 29;
6 and 7 in base 6 are 10 and 11 and concat(10,11) = 1011 in base 10 is 223.

Crossrefs

Cf. A000040, A030458.

Programs

  • Maple
    with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; a:=convert(q+1,base,h); b:=convert(q,base,h); c:=[op(a),op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i,6),i=1..1000);
  • Mathematica
    With[{b = 6}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 360, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)

A287308 Primes that can be generated by the concatenation in base 7, in ascending order, of two consecutive integers read in base 10.

Original entry on oeis.org

17, 41, 401, 601, 701, 751, 1051, 1151, 1201, 1301, 1451, 1601, 1801, 1901, 1951, 2251, 2351, 18233, 19609, 20297, 20641, 21673, 25457, 25801, 26489, 26833, 31649, 33713, 34057, 35089, 36809, 38873, 39217, 41281, 41969, 46441, 47129, 49193, 49537, 51257, 52289
Offset: 1

Views

Author

Paolo P. Lava, May 23 2017

Keywords

Examples

			2 and 3 in base 7 are 2 and 3 and concat(2,3) = 23 in base 10 is 17;
8 and 9 in base 7 are 11 and 12 and concat(11,12) = 1112 in base 10 is 401.

Crossrefs

Cf. A000040, A030458.

Programs

  • Maple
    with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; a:=convert(q+1,base,h); b:=convert(q,base,h); c:=[op(a),op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i,7),i=1..1000);
  • Mathematica
    With[{b = 7}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 160, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)

A287312 Primes that can be generated by the concatenation in base 9, in ascending order, of two consecutive integers read in base 10.

Original entry on oeis.org

11, 31, 41, 61, 71, 739, 821, 1231, 1559, 1723, 2297, 2543, 2707, 2789, 2953, 3527, 3691, 4019, 5003, 5167, 5413, 5659, 5741, 5987, 6151, 6397, 65701, 66431, 67891, 72271, 76651, 81031, 81761, 83221, 85411, 100741, 102931, 108041, 121181, 135781, 136511, 140891
Offset: 1

Views

Author

Paolo P. Lava, May 24 2017

Keywords

Examples

			1 and 2 in base 9 are 1 and 2 and concat(1,2) = 12 in base 10 is 11;
9 and 10 in base 9 are 10 and 11 and concat(10,11) = 1011 in base 10 is 739.

Crossrefs

Cf. A000040, A030458.

Programs

  • Maple
    with(numtheory): P:= proc(q,h) local a,b,c,d,k,n; a:=convert(q+1,base,h); b:=convert(q,base,h); c:=[op(a),op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i,9),i=1..1000);
  • Mathematica
    With[{b = 9}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 200, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 25 2017 *)
Previous Showing 31-34 of 34 results.

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