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 1-10 of 10 results.

A028373 Numbers that have only the straight digits {1, 4, 7}.

Original entry on oeis.org

1, 4, 7, 11, 14, 17, 41, 44, 47, 71, 74, 77, 111, 114, 117, 141, 144, 147, 171, 174, 177, 411, 414, 417, 441, 444, 447, 471, 474, 477, 711, 714, 717, 741, 744, 747, 771, 774, 777, 1111, 1114, 1117, 1141, 1144, 1147, 1171, 1174, 1177, 1411, 1414, 1417, 1441
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A028374, the curved sequence.
Cf. A079651 prime numbers using only the straight digits 1,4,7.

Programs

  • Maple
    a:= proc(n) local d, i, m, r; m:=n; r:=0;
      for i from 0 while m>0 do
        d:= irem(m, 3, 'm');
        if d=0 then d:=3; m:=m-1 fi;
        r:= r+10^i*[1, 4, 7][d]
      od: r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 25 2014
  • Mathematica
    f[n_] := Block[{id = IntegerDigits[n], straight = {1, 4, 7}}, If[ Union[ Join[id, straight]] == straight, True, False]]; Select[ Range[0, 1446], f[ # ] & ]
FromDigits/@Flatten[Table[Tuples[{1,4,7},n],{n,4}],1] (* Harvey P. Dale, Jul 25 2015 *)
  • PARI
    is(n)=my(t);while(n,t=n%10;if(t!=1&&t!=4&&t!=7,return(0));n\=10);!!t \\ Charles R Greathouse IV, Sep 25 2012

A034470 Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9.

Original entry on oeis.org

2, 3, 5, 23, 29, 53, 59, 83, 89, 223, 229, 233, 239, 263, 269, 283, 293, 353, 359, 383, 389, 503, 509, 523, 563, 569, 593, 599, 653, 659, 683, 809, 823, 829, 839, 853, 859, 863, 883, 929, 953, 983, 2003, 2029, 2039, 2053, 2063, 2069, 2083, 2089, 2099, 2203
Offset: 1

Views

Author

Robert G. Wilson v, Jan 24 2003

Keywords

Comments

Intersection of A000040 and A028374. - K. D. Bajpai, Sep 07 2014

Examples

			From _K. D. Bajpai_, Sep 07 2014: (Start)
29 is prime and is composed only of the curved digits 2 and 9.
359 is prime and is composed only of the curved digits 3, 5 and 9.
(End)
20235869 is the smallest instance using all curved digits. - _Michel Marcus_, Sep 07 2014

Links

Crossrefs

Cf. A028374, A072960, A079652.

Programs

  • Maple
    N:= 4: # to get all entries with at most N digits
S:= {0,2,3,5,6,8,9}:
T:= S:
for j from 2 to N do
T:= map(t -> seq(10*t+s,s=S),T);
od:
select(isprime,T);
# In Maple 11 and earlier, uncomment the next line:
# sort(convert(%,list)); # Robert Israel, Sep 07 2014
  • Mathematica
    Select[Range[2222], PrimeQ[#] && Union[Join[IntegerDigits[#], {0, 2, 3, 5, 6, 8, 9}]] == {0, 2, 3, 5, 6, 8, 9} &] (* RGWv *)
Select[Prime[Range[500]], Intersection[IntegerDigits[#], {1, 4, 7}] == {} &] (* K. D. Bajpai, Sep 07 2014 *)

A079652 Prime numbers using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

3, 83, 89, 383, 389, 683, 809, 839, 863, 883, 983, 3083, 3089, 3389, 3803, 3833, 3863, 3889, 3989, 6089, 6389, 6689, 6803, 6833, 6863, 6869, 6883, 6899, 6983, 8009, 8039, 8069, 8089, 8093, 8363, 8369, 8389, 8609, 8663, 8669, 8689, 8693, 8699, 8803, 8839
Offset: 1

Views

Author

Shyam Sunder Gupta, Jan 23 2003

Keywords

Comments

Intersection of A000040 and A072960. - K. D. Bajpai, Sep 01 2014

Links

Crossrefs

Cf. A072960, A028374.
Cf. A034470.

Programs

  • Maple
    N:= 4: # to get all terms with up to N digits
Digs:= {0,3,6,8,9}:
A:= NULL:
for d from 1 to N do
  C:= combinat[cartprod]([Digs minus {0},Digs $(d-1)]);
  while not C[finished] do
    L:= C[nextvalue]();
    x:= add(L[i]*10^(d-i),i=1..d);
    if isprime(x) then A:= A,x fi
  od
od:
A; # Robert Israel, Aug 31 2014
  • Mathematica
    Select[ Range[8850], PrimeQ[ # ] && Union[ Join[ IntegerDigits[ # ], {0, 3, 6, 8, 9}]] == {0, 3, 6, 8, 9} &]
Select[Prime[Range[5000]], Intersection[IntegerDigits[#], {1, 2, 4, 5, 7}] == {} &] (* K. D. Bajpai, Sep 01 2014 *)
Select[FromDigits/@Tuples[{0,3,6,8,9},4],PrimeQ] (* Harvey P. Dale, Sep 05 2022 *)

A082741 Numbers that have digits consisting only of line segments or both line segments and curves (base 10 digits are 1, 2, 4, 5, 7).

Original entry on oeis.org

1, 2, 4, 5, 7, 11, 12, 14, 15, 17, 21, 22, 24, 25, 27, 41, 42, 44, 45, 47, 51, 52, 54, 55, 57, 71, 72, 74, 75, 77, 111, 112, 114, 115, 117, 121, 122, 124, 125, 127, 141, 142, 144, 145, 147, 151, 152, 154, 155, 157, 171, 172, 174, 175, 177, 211, 212, 214, 215, 217, 221
Offset: 1

Views

Author

Rick L. Shepherd, May 21 2003

Keywords

Comments

This sequence allows the digits 2 and 5, formed from combinations of line segments and curves; the subsequence A028373 does not.

Links

Crossrefs

Cf. A028373 (line-segment digits 1, 4, 7 only), A028374 (digits with curves or both curves and line segments), A072960 (curved digits 0, 3, 6, 8, 9 only).

Programs

  • Maple
    a:= proc(n) local d, i, m, r; m:=n; r:=0;
      for i from 0 while m>0 do
        d:= irem(m, 5, 'm');
        if d=0 then d:=5; m:=m-1 fi;
        r:= r+10^i*[1, 2, 4, 5, 7][d]
      od: r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 25 2014
  • Mathematica
    Table[FromDigits/@Tuples[{1,2,4,5,7},n],{n,3}]//Flatten (* Harvey P. Dale, Apr 17 2022 *)

A079064 a(n) is the next available entirely straight or curved number, depending on whether n contains a straight digit or not.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 17, 41, 44, 47, 71, 74, 77, 111, 200, 411, 500, 502, 711, 800, 802, 1111, 2000, 2002, 2003, 4111, 5000, 5002, 7111, 8000, 8002, 11111, 20000, 20002, 41111, 41114, 41117, 41141, 41144, 41147, 41171, 41174, 41177, 41411, 50000
Offset: 0

Views

Author

Jon Perry, Feb 02 2003

Keywords

Examples

			a(10) must be the first entirely straight number greater than 9, as 1 is straight, therefore a(10)=11.
a(20) must be the first entirely curved number greater than 111, therefore a(20)=200.

Links

Crossrefs

Cf. A028373 (straight numbers), A028374 (curved numbers), A079170.

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010
a(35) and beyond from David Consiglio, Jr., Oct 31 2023

A079170 a(n) is the next available entirely straight or curved number, depending on whether n contains a curved digit or not.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 41, 50, 52, 71, 80, 82, 111, 200, 202, 203, 205, 206, 208, 209, 220, 222, 223, 225, 226, 228, 229, 230, 232, 233, 235, 236, 238, 239, 250, 252, 411, 500, 502, 711, 800, 802, 1111, 2000, 2002, 2003, 2005, 2006, 2008, 2009, 2020
Offset: 0

Views

Author

Jon Perry, Feb 03 2003

Keywords

Examples

			a(10) must be the first entirely curved number greater than 9, as 0 is curved, therefore a(10)=20.
a(17) must be the first entirely straight number greater than 82, therefore a(20)=111.

Links

Crossrefs

Cf. A028373 (straight numbers), A028374 (curved numbers), A079064.

Extensions

a(33) and beyond from David Consiglio, Jr., Oct 31 2023

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 *)

A242756 Semiprimes having only the curved digits.

Original entry on oeis.org

6, 9, 22, 25, 26, 33, 35, 38, 39, 55, 58, 62, 65, 69, 82, 85, 86, 93, 95, 202, 203, 205, 206, 209, 226, 235, 253, 259, 262, 265, 289, 295, 298, 299, 302, 303, 305, 309, 323, 326, 329, 335, 339, 355, 358, 362, 365, 382, 386, 393, 395, 398, 502, 505, 526, 529, 533
Offset: 1

Views

Author

K. D. Bajpai, May 22 2014

Keywords

Comments

A curved-digit semiprime has only the curved digits, i.e., 0, 2, 3, 5, 6, 8 or 9.

Examples

			358 = 2 * 179 is semiprime having only the curved digits 3, 5 and 8. Hence appears in the sequence.
689 = 13 * 53 is semiprime having only the curved digits 6, 8 and 9. Hence appears in the sequence.

Links

Crossrefs

Cf. A028374, A001358, A034470.

Programs

  • Mathematica
    A242756 = {}; Do[a = PrimeOmega[n];If[a == 2 && Intersection[IntegerDigits[n], {1, 4, 7}] == {}, AppendTo[A242756, n]], {n, 1000}]; A242756
  • PARI
    s=[]; for(n=1, 600, if(bigomega(n)==2 && setintersect(vecsort(digits(n), , 8), [1,4,7])==[], s=concat(s, n))); s \\ Colin Barker, Jun 03 2014

A247016 Triangular numbers A000217 composed of only curved digits {0, 2, 3, 5, 6, 8, 9}.

Original entry on oeis.org

0, 3, 6, 28, 36, 55, 66, 253, 300, 325, 528, 595, 630, 666, 820, 903, 990, 2080, 2556, 2628, 2850, 2926, 3003, 3655, 3828, 5050, 5253, 5356, 5565, 5886, 5995, 6328, 6555, 6903, 8256, 8385, 20503, 22366, 23005, 23220, 23653, 25200, 26335, 26565, 28203, 28680, 28920
Offset: 1

Views

Author

K. D. Bajpai, Sep 09 2014

Keywords

Comments

Intersection of A000217 and A028374.

Examples

			a(10) = 528 is in the sequence because it is A000217(32) and composed of only curved digits 5, 2 and 8.
a(14) = 820 is in the sequence because it is A000217(40) and composed of only curved digits 8, 2 and 0.

Links

Crossrefs

Cf. A000217, A028374, A034470, A072960.

Programs

  • Mathematica
    A247016 = {}; Do[t = n*(n + 1)/2; If[Intersection[IntegerDigits[t], {1, 4, 7}] == {}, AppendTo[A247016, t]], {n,0, 500}]; A247016
Select[Accumulate[Range[0,300]],DigitCount[#,10,1]==DigitCount[#,10,4] == DigitCount[ #,10,7] == 0&] (* Harvey P. Dale, Apr 18 2019 *)
  • Python
    for n in range(2,10**3):
  s = str(int(n*(n-1)/2))
  if not (s.count('1') + s.count('4') + s.count('7')):
    print(int(s),end=', ') # Derek Orr, Sep 18 2014

Extensions

Added starting number 0 (suggested by D. Orr), added A-number in the name and examples. - Wolfdieter Lang, Oct 06 2014

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 1-10 of 10 results.

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