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 21-28 of 28 results.

A257223 Numbers that have at least one divisor containing the digit 6 in base 10.

Original entry on oeis.org

6, 12, 16, 18, 24, 26, 30, 32, 36, 42, 46, 48, 52, 54, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 76, 78, 80, 84, 86, 90, 92, 96, 102, 104, 106, 108, 112, 114, 116, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 144, 146, 150, 152, 156, 160, 161, 162
Offset: 1

Views

Author

Jaroslav Krizek, May 05 2015

Keywords

Comments

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 6.
A011536 (numbers that contain a 6) is a subsequence. - Michel Marcus, May 25 2015

Examples

			18 is in sequence because the list of divisors of 18: (1, 2, 3, 6, 9, 18) contains digit 6.

Crossrefs

Cf. A037278, A176558, A243360, A256824.
Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257224 (7), A257225 (8), A257226 (9).

Programs

  • Magma
    [n: n in [1..1000] | [6] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];
  • Mathematica
    Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 6] > 0 &]
Select[Range[200],Count[Flatten[IntegerDigits/@Divisors[#]],6]>0&] (* Harvey P. Dale, Nov 05 2021 *)
  • PARI
    is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 6), return(1))); 0

Formula

a(n) ~ n.

Extensions

Mathematica and PARI programs with assistance from Michael De Vlieger and Charles R Greathouse IV, respectively.

A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 102, 111, 120, 123, 132, 135, 147, 153, 159, 174, 195, 201, 204, 210, 213, 222, 231, 234, 240, 243, 246, 258, 264, 285, 306, 312, 315, 321, 324, 333, 342, 345, 351, 354, 357, 360, 369, 375, 396, 402
Offset: 1

Views

Author

Claudio Meller, Aug 09 2010

Keywords

Comments

Subsequence of A061383.
A180160(a(n)) = 0. - Reinhard Zumkeller, Aug 15 2010

Examples

			135 is in the list because (1+3+5)/3 = 3 and 3 is a digit of 135.

Links

Crossrefs

Cf. A007953, A055642, A004426, A004427; A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539.
Cf. A052018. - Reinhard Zumkeller, Aug 15 2010

Programs

  • Haskell
    a175688 n = a175688_list !! (n-1)
a175688_list = filter f [0..] where
   f x = m == 0 && ("0123456789" !! avg) `elem` show x
         where (avg, m) = divMod (a007953 x) (a055642 x)
-- Reinhard Zumkeller, Jun 18 2013
  • Mathematica
    idQ[n_]:=Module[{idn=IntegerDigits[n],m},m=Mean[idn];IntegerQ[m] && MemberQ[idn,m]]; Select[Range[0,500],idQ] (* Harvey P. Dale, Jun 10 2011 *)

Extensions

Edited by Reinhard Zumkeller, Aug 13 2010

A284291 Primes containing a digit 6.

Original entry on oeis.org

61, 67, 163, 167, 263, 269, 367, 461, 463, 467, 563, 569, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 761, 769, 863, 967, 1061, 1063, 1069, 1163, 1361, 1367, 1567, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663
Offset: 1

Views

Author

Jaroslav Krizek, Mar 24 2017

Keywords

Comments

Subsequence of A011536 and A062673.

Links

Crossrefs

Primes containing a digit k for k = 0 - 9: A056709 (k = 0), A208270 (k = 1), A208272 (k = 2), A212525 (k = 3), A284290 (k = 4), A257667 (k = 5), A284291 (k = 6), A257668 (k = 7), A284292 (k = 8), A106093 (k = 9).

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | 6 in Intseq(p)];
  • Mathematica
    Select[Range[2000], PrimeQ[#] && MemberQ[IntegerDigits[#], 6] &] (* Amiram Eldar, Nov 09 2019 *)

A043514 Numbers having two 6's in base 10.

Original entry on oeis.org

66, 166, 266, 366, 466, 566, 606, 616, 626, 636, 646, 656, 660, 661, 662, 663, 664, 665, 667, 668, 669, 676, 686, 696, 766, 866, 966, 1066, 1166, 1266, 1366, 1466, 1566, 1606, 1616, 1626, 1636, 1646, 1656, 1660, 1661, 1662, 1663
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Subsequence of A011536.

Programs

  • Mathematica
    Select[Range[2000],DigitCount[#,10,6]==2&]  (* Harvey P. Dale, Mar 23 2011 *)

A043516 Numbers having four 6's in base 10.

Original entry on oeis.org

6666, 16666, 26666, 36666, 46666, 56666, 60666, 61666, 62666, 63666, 64666, 65666, 66066, 66166, 66266, 66366, 66466, 66566, 66606, 66616, 66626, 66636, 66646, 66656, 66660, 66661, 66662, 66663, 66664, 66665, 66667
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Subsequence of A011536.

Programs

  • Mathematica
    Select[Range[70000],DigitCount[#,10,6]==4&] (* Harvey P. Dale, Sep 17 2023 *)

A245877 Primes p such that p - d and p + d are also primes, where d is the largest digit of p.

Original entry on oeis.org

263, 563, 613, 653, 1613, 1663, 3463, 4643, 5563, 5653, 6263, 6323, 12653, 13463, 14633, 16063, 16223, 21163, 21563, 25463, 26113, 30643, 32063, 33623, 36313, 41263, 41603, 44263, 53623, 54623, 56003, 60133, 61553, 62213, 62633, 64013, 65413, 105613, 106213
Offset: 1

Views

Author

Colin Barker, Aug 05 2014

Keywords

Comments

Intersection of A245742 and A245743.
The largest digit of a(n) is 6, and the least significant digit of a(n) is 3.
Intersection of A006489, A011536, and complements of A011537, A011538, A011539. - Robert Israel, Aug 05 2014

Examples

			The prime 263 is in the sequence because 263 - 6 = 257 and 263 + 6 = 269 are both primes.

Links

Crossrefs

Cf. A006489, A245742, A245743, A245744, A245745, A245878.

Programs

  • Mathematica
    pdpQ[n_]:=Module[{m=Max[IntegerDigits[n]]},AllTrue[n+{m,-m},PrimeQ]]; Select[ Prime[Range[11000]],pdpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 13 2017 *)
  • PARI
    select(p->d=vecsort(digits(p),,4)[1]; isprime(p-d) && isprime(p+d), primes(20000))
  • Python
    import sympy
from sympy import prime
from sympy import isprime
for n in range(1,10**5):
  s=prime(n)
  lst = []
  for i in str(s):
    lst.append(int(i))
  if isprime(s+max(lst)) and isprime(s-max(lst)):
    print(s,end=', ')
# Derek Orr, Aug 13 2014

A095790 Numbers whose name in English contains an "r".

Original entry on oeis.org

3, 4, 13, 14, 23, 24, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 53, 54, 63, 64, 73, 74, 83, 84, 93, 94, 103, 104, 113, 114, 123, 124, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Comments

A008520 are numbers which contain an "e", A008540 an "f", A011538 a "g", A008536 an "n", A008519 an "o", A008538 an "s", A008522 a "t", A011534 a "u", A011532 a "w", A011536 an "x" and A008553 a "y"

Examples

			a(1) = 3 because "three" contains an "r", 0, 1 and 2 do not

Crossrefs

Cf. A008520, A008540, A011538, A008536, A008519, A008538, A008522, A011534, A011532, A011536, A008553.

A095798 Numbers whose name in English contains a "v".

Original entry on oeis.org

5, 7, 11, 12, 17, 25, 27, 35, 37, 45, 47, 55, 57, 65, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 87, 95, 97, 105, 107, 111, 112, 117, 125, 127, 135, 137, 145, 147, 155, 157, 165, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 185, 187, 195, 197, 205, 207
Offset: 1

Views

Author

Michael Joseph Halm, Jul 10 2004

Keywords

Comments

A008520 are numbers which contain an "e", A008540 an "f", A011538 a "g", A008536 an "n", A008519 an "o", A008538 an "s", A008522 a "t", A011534 a "u", A011532 a "w", A011536 an "x" and A008553 a "y"

Examples

			a(3) = 11 because "eleven" contains a "v" and it is the third number to do so (after "five" and "seven").

Crossrefs

Cf. A008520, A008540, A011538, A008536, A008519, A008538, A008522, A011534, A011532, A011536, A008553.

Extensions

Corrected by Rick L. Shepherd, Jul 10 2004
Previous Showing 21-28 of 28 results.

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