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 1-4 of 4 results.

A028374 Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}.

Original entry on oeis.org

0, 2, 3, 5, 6, 8, 9, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 200, 202, 203, 205, 206, 208, 209, 220, 222, 223, 225, 226, 228, 229, 230, 232, 233
Offset: 1

Views

Author

Greg Heil (gheil(AT)scn.org), Dec 11 1999

Keywords

Comments

From Bernard Schott, Mar 26 2023: (Start)
Previous name was: "Curved numbers: numbers that have only curved digits (0, 2, 3, 5, 6, 8, 9)"; but in fact, the curved numbers form the sequence A072960.
This sequence allows all digits except for 1, 4 and 7. (End)

Examples

			From _K. D. Bajpai_, Sep 07 2014: (Start)
206 is in the sequence because it has only curved digits 2, 0 and 6.
208 is in the sequence because it has only curved digits 2, 0 and 8.
2035689 is the smallest number having all the curved digits.
(End)

Links

Crossrefs

Cf. A028373 (straight digits: 1, 4, 7), A072960 (curved digits: 0, 3, 6, 8, 9), A072961 (both straight and curved digits: 2, 5).
Combinations: A082741 (digits: 1, 2, 4, 5, 7), A361780 (digits: 0, 1, 3, 4, 6, 7, 8, 9).
Cf. A034470 (subsequence of primes).

Programs

  • Magma
    [n: n in [0..300] | Set(Intseq(n)) subset [0,2,3,5, 6,8,9] ]; // Vincenzo Librandi, Sep 19 2014
  • Maple
    N:= 3: S:= {0, 2, 3, 5, 6, 8, 9}: K:= S:
for j from 2 to N do
     K:= map(t -> seq(10*t+s, s=S), K);
         od:
print( K);  # K. D. Bajpai, Sep 07 2014
  • Mathematica
    f[n_] := Block[{id = IntegerDigits[n], curve = {0, 2, 3, 5, 6, 8, 9}}, If[ Union[ Join[id, curve]] == curve, True, False]]; Select[ Range[0, 240], f[ # ] & ]
Select[Range[0, 249], Union[DigitCount[#] * {1, 0, 0, 1, 0, 0, 1, 0, 0, 0}] == {0} &] (* Alonso del Arte, May 23 2014 *)
Select[Range[0,500],Intersection[IntegerDigits[#],{1,4,7}]=={}&] (* K. D. Bajpai, Sep 07 2014 *)
  • Python
    for n in range(10**3):
  s = str(n)
  if not (s.count('1') + s.count('4') + s.count('7')):
    print(n,end=', ') # Derek Orr, Sep 19 2014

Extensions

Corrected and extended by Rick L. Shepherd, May 21 2003
Offset corrected by Arkadiusz Wesolowski, Aug 15 2011
Definition clarified by Bernard Schott, Mar 25 2023

A247052 Primes composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}.

Original entry on oeis.org

2, 5, 7, 11, 17, 41, 47, 71, 127, 151, 157, 211, 227, 241, 251, 257, 271, 277, 421, 457, 521, 541, 547, 557, 571, 577, 727, 751, 757, 1117, 1151, 1171, 1217, 1277, 1427, 1447, 1451, 1471, 1511, 1571, 1721, 1741, 1747, 1777, 2111, 2141, 2221, 2251, 2411, 2417
Offset: 1

Views

Author

K. D. Bajpai, Sep 10 2014

Keywords

Comments

Intersection of A000040 and A082741.

Examples

			127 is in the sequence because it is prime and composed of digits 1, 2 and 7 only.
1427 is in the sequence because it is prime and composed of digits 1, 2, 4 and 7 only.
a(129) = 12457 is the smallest prime using all the digits 1, 2, 4, 5 and 7 only once.

Links

Crossrefs

Cf. A000040, A082741.

Programs

  • Magma
    [NthPrime(n): n in [1..400] | Set(Intseq(NthPrime(n))) subset [1,2,4,5,7] ]; // Vincenzo Librandi, Sep 19 2014
  • Mathematica
    Select[Prime[Range[500]], Intersection[IntegerDigits[#], {0, 3, 6, 8, 9}] == {} &]
  • Python
    from sympy import prime
for n in range(1,10**3):
  s = str(prime(n))
  if not (s.count('0') + s.count('3') + s.count('6') + s.count('8') + s.count('9')):
    print(s,end=', ') # Derek Orr, Sep 18 2014

A361780 Numbers that have digits consisting only of line segments {1, 4, 7} or curved digits {0, 3, 6, 8, 9}.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 30, 31, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 60, 61, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110
Offset: 1

Views

Author

Bernard Schott, Mar 23 2023

Keywords

Comments

This sequence allows all digits except for 2 and 5.

Crossrefs

Cf. A028373 (line-segment digits: {1, 4, 7}), A072960 (curved digits: {0, 3, 6, 8, 9}), A072961 (both line segments and curves digits: {2, 5}).
Cf. A082741 (digits: {1, 2, 4, 5, 7}), A028374 (digits: {0, 2, 3, 5, 6, 8, 9}), this sequence (digits {0, 1, 3, 4, 6, 7, 8, 9}).

Programs

  • Mathematica
    Select[Range[0, 110], AllTrue[IntegerDigits[#], ! MemberQ[{2, 5}, #1] &] &] (* Amiram Eldar, Mar 24 2023 *)

A247021 Triangular numbers composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}.

Original entry on oeis.org

1, 15, 21, 45, 55, 171, 741, 1225, 1275, 1711, 2145, 2211, 2415, 2775, 5151, 11175, 15225, 21115, 22155, 25425, 44551, 45451, 72771, 77421, 112575, 121771, 124251, 125751, 151525, 211575, 221445, 222111, 224115, 227475, 254541, 255255, 417241, 451725, 551775, 577275
Offset: 1

Views

Author

K. D. Bajpai, Sep 09 2014

Keywords

Comments

Intersection of A000217 and A082741.
Every term is congruent to 1 mod 10 or 5 mod 10. - Derek Orr, Sep 19 2014

Examples

			1275 is a term because 1275 = 50 * (50 + 1) / 2, is a triangular number composed of digits 1, 2, 7 and 5.
2145 is a term because 2145 = 65 * (65 + 1) / 2, is a triangular number composed of digits 1, 2, 4 and 5.
a(38) = 451725 is the first occurrence of triangular number using each digit 1, 2, 4, 5 or 7 at least once.

Links

Crossrefs

Cf. A000217, A028373, A028374, A082741, A119033.

Programs

  • Mathematica
    A247021 = {}; Do[t = n*(n + 1)/2; If[Intersection[IntegerDigits[t], {0, 3, 6, 8, 9}] == {}, AppendTo[A247021, t]], {n, 1000}]; A247021
Select[Accumulate[Range[1500]],SubsetQ[{1,2,4,5,7}, IntegerDigits[#]]&] (* Harvey P. Dale, May 20 2025 *)
  • Python
    for n in range(10**3):
  s = str(int(n*(n+1)/2))
  if not (s.count('0') + s.count('3') + s.count('6') + s.count('8') + s.count('9')):
    print(int(s), end=', ') # Derek Orr, Sep 19 2014
Showing 1-4 of 4 results.

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