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 1-8 of 8 results.

A208259 Numbers starting and ending with digit 1.

Original entry on oeis.org

1, 11, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 1001, 1011, 1021, 1031, 1041, 1051, 1061, 1071, 1081, 1091, 1101, 1111, 1121, 1131, 1141, 1151, 1161, 1171, 1181, 1191, 1201, 1211, 1221, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1301, 1311, 1321, 1331
Offset: 1

Views

Author

Jaroslav Krizek, Feb 24 2012

Keywords

Comments

A000030(a(n)) = a(n) mod 10 = 1. - Reinhard Zumkeller, Jul 16 2014

Links

Crossrefs

Intersection of A017281 and A131835. Union of A062332 and A208260.
Supersequence of A208262 (numbers with all divisors starting and ending with digit 1).
Cf. A062332 (primes starting and ending with a digit 1), A208260 (nonprime numbers starting and ending with a digit 1).
Cf. A017281, A131835, A000030.

Programs

  • Haskell
    a208259 n = a208259_list !! (n-1)
a208259_list = 1 : map ((+ 1) . (* 10)) a131835_list
-- Reinhard Zumkeller, Jul 16 2014
  • Mathematica
    Select[Range[2000], First[IntegerDigits[#]] == 1 && Last[IntegerDigits[#]] == 1 &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2012 *)

A208261 Nonprime numbers with all divisors starting and ending with digit 1.

Original entry on oeis.org

1, 121, 1111, 1331, 1441, 1661, 1991, 10201, 11231, 11341, 11561, 11671, 12001, 12221, 12661, 12881, 12991, 13211, 13231, 13541, 14201, 14311, 14531, 14641, 14971, 15191, 15251, 15851, 15961, 16181, 16291, 16621, 16841, 17161, 17281, 17611, 17831, 18271, 18281
Offset: 1

Views

Author

Jaroslav Krizek, Feb 24 2012

Keywords

Comments

Complement of A062332 with respect to A208262. Subsequence of A208260 (nonprime numbers starting and ending with digit 1).

Examples

			Divisors of 1111: 1, 11, 101, 1111.

Links

Crossrefs

Cf. A208262 (numbers with all divisors starting and ending with digit 1), A062332 (primes starting and ending with digit 1).

Programs

  • Mathematica
    Select[Table[n, {n, 20000}], ! PrimeQ[#] && Union[First /@ IntegerDigits[Divisors[#]]] == {1} && Union[Last /@ IntegerDigits[Divisors[#]]] == {1} &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2012 *)
d1Q[n_]:=Module[{idn=IntegerDigits[n]},First[idn]==Last[idn]==1]; Select[ Range[1,20000,10],!PrimeQ[#]&&Count[Divisors[#],?d1Q] == DivisorSigma[ 0,#]&] (* _Harvey P. Dale, Nov 23 2012 *)

A062333 Primes starting and ending with 3.

Original entry on oeis.org

3, 313, 353, 373, 383, 3023, 3083, 3163, 3203, 3253, 3313, 3323, 3343, 3373, 3413, 3433, 3463, 3533, 3583, 3593, 3613, 3623, 3643, 3673, 3733, 3793, 3803, 3823, 3833, 3853, 3863, 3923, 3943, 30013, 30103, 30113, 30133, 30203, 30223, 30253, 30293
Offset: 1

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Comments

Intersection of A045709 and A030431. - Michel Marcus, Jun 08 2013

Examples

			3413 is a member, as it is a prime and the first and the last digits are both 3.

Links

Crossrefs

Cf. A062332, A062334, A062335.

Programs

  • Mathematica
    se3Q[n_]:=Module[{idn=IntegerDigits[n]},idn[[1]]==idn[[-1]]==3]; Select[ Prime[ Range[3300]],se3Q] (* Harvey P. Dale, Jul 24 2019 *)
  • PARI
    { n=-1; t=log(10); forprime (p=2, 5*10^5, if ((p-10*(p\10)) == 3 && (p\10^(log(p)\t)) == 3, write("b062333.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 29 2001
Offset changed by Andrew Howroyd, Sep 17 2024

A062334 Primes starting and ending with 7.

Original entry on oeis.org

7, 727, 757, 787, 797, 7027, 7057, 7127, 7177, 7187, 7207, 7237, 7247, 7297, 7307, 7417, 7457, 7477, 7487, 7507, 7517, 7537, 7547, 7577, 7607, 7687, 7717, 7727, 7757, 7817, 7867, 7877, 7907, 7927, 7937, 70067, 70117, 70157, 70177, 70207, 70237
Offset: 1

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Examples

			7687 is a member, as it is a prime and the first and the last digits are both 7.

Links

Crossrefs

Cf. A062332, A062333, A062335.

Programs

  • PARI
    { default(primelimit, 800000); n=-1; t=log(10); forprime (p=2, 800000, if ((p-10*(p\10)) == 7 && (p\10^(log(p)\t)) == 7, write("b062334.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 29 2001
Offset changed by Andrew Howroyd, Sep 17 2024

A062335 Primes starting and ending with 9.

Original entry on oeis.org

919, 929, 9029, 9049, 9059, 9109, 9199, 9209, 9239, 9319, 9349, 9419, 9439, 9479, 9539, 9619, 9629, 9649, 9679, 9689, 9719, 9739, 9749, 9769, 9829, 9839, 9859, 9929, 9949, 90019, 90059, 90089, 90149, 90199, 90239, 90289, 90359, 90379, 90439
Offset: 1

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Examples

			9679 is a member, as it is a prime and the first and the last digits are both 9.

Links

Crossrefs

Cf. A062332, A062333, A062334.

Programs

  • Mathematica
    fl9Q[n_]:=IntegerDigits[n][[1]]==IntegerDigits[n][[-1]]==9; Select[ Prime[ Range[10000]],fl9Q] (* Harvey P. Dale, Dec 31 2019 *)
  • PARI
    { default(primelimit, 10^6); n=-1; t=log(10); forprime (p=2, 10^6, if ((p-10*(p\10)) == 9 && (p\10^(log(p)\t)) == 9, write("b062335.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 29 2001
Offset changed by Andrew Howroyd, Sep 17 2024

A208260 Nonprime numbers starting and ending with digit 1.

Original entry on oeis.org

1, 111, 121, 141, 161, 171, 1001, 1011, 1041, 1071, 1081, 1101, 1111, 1121, 1131, 1141, 1161, 1191, 1211, 1221, 1241, 1251, 1261, 1271, 1281, 1311, 1331, 1341, 1351, 1371, 1391, 1401, 1411, 1421, 1431, 1441, 1461, 1491, 1501, 1521, 1541, 1551, 1561, 1581, 1591
Offset: 1

Views

Author

Jaroslav Krizek, Feb 24 2012

Keywords

Comments

Complement of A062332 with respect to A208259. Supersequence of A208261 (nonprime numbers with all divisors starting and ending with digit 1).

Links

Crossrefs

Cf. A208259 (number starting and ending with a number 1), A062332 (primes starting and ending with a number 1).
Cf. A010051, A017281, A131835, A000030.

Programs

  • Haskell
    a208260 n = a208260_list !! (n-1)
a208260_list = filter ((== 0) . a010051') a208259_list
-- Reinhard Zumkeller, Jul 16 2014
  • Mathematica
    Select[Range[2000], ! PrimeQ[#] && First[IntegerDigits[#]] == 1 && Last[IntegerDigits[#]] == 1 &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2012 *)
Join[{1},Select[Range[2000],CompositeQ[#]&&NumberDigit[#,0] == NumberDigit[ #,IntegerLength[ #]-1]==1&]] (* Harvey P. Dale, Aug 01 2021 *)

Formula

(1 - A010051(a(n))) * A000030(a(n)) * (a(n) mod 10) = 1. - Reinhard Zumkeller, Jul 16 2014

A208262 Numbers with all divisors starting and ending with digit 1.

Original entry on oeis.org

1, 11, 101, 121, 131, 151, 181, 191, 1021, 1031, 1051, 1061, 1091, 1111, 1151, 1171, 1181, 1201, 1231, 1291, 1301, 1321, 1331, 1361, 1381, 1441, 1451, 1471, 1481, 1511, 1531, 1571, 1601, 1621, 1661, 1721, 1741, 1801, 1811, 1831, 1861, 1871, 1901, 1931, 1951, 1991
Offset: 1

Views

Author

Jaroslav Krizek, Feb 24 2012

Keywords

Comments

Union of A062332 and A208261. Subsequence of A208259 (numbers starting and ending with digit 1).

Examples

			Divisors of 1111: 1, 11, 101, 1111.

Crossrefs

Cf. A062332 (primes starting and ending with digit 1), A208261 (nonprime numbers with all divisors starting and ending with digit 1).

Programs

  • Mathematica
    Select[Table[n, {n, 2000}], Union[First /@ IntegerDigits[Divisors[#]]] == {1} && Union[Last /@ IntegerDigits[Divisors[#]]] == {1} &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2012 *)

A178318 Primes which remain prime after reflection across a vertical line through the middle of the number (numbers are written as digital clock style numerals).

Original entry on oeis.org

2, 5, 11, 101, 181, 1051, 1181, 1201, 1811, 10151, 11251, 11551, 12101, 12211, 12511, 15121, 18181, 100151, 100501, 101501, 101581, 102001, 102101, 102181, 102551, 105211, 105251, 108881, 110051, 110581, 110881, 111521, 111581, 115021, 115201
Offset: 1

Views

Author

David Nacin, May 24 2010

Keywords

Comments

Apart from first two terms: subsequence of A208259. - Reinhard Zumkeller, Jul 16 2014

Examples

			For example 1051 becomes 1201 under this reflection and since these are both prime, these number are part of the sequence. Note that a number must be composed only of the digits 0,1,2,5,8 to qualify.

Links

Crossrefs

Cf. A125308, A178317.
Cf. A010051, A004086, A208259, A062332.

Programs

  • Haskell
    import Data.List (intersect, genericIndex)
a178318 n = a178318_list !! (n-1)
a178318_list = 2 : 5 : filter f a062332_list where
   f p = null (show p `intersect` "34679") && a010051' (r 0 p) == 1
   r y 0 = y
   r y x = r (10 * y + genericIndex [0,1,5,0,0,2,0,0,8,0] d) x'
             where (x', d) = divMod x 10
-- Reinhard Zumkeller, Jul 16 2014
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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