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 1-3 of 3 results.

A062332 Primes starting and ending with 1.

Original entry on oeis.org

11, 101, 131, 151, 181, 191, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291, 1301, 1321, 1361, 1381, 1451, 1471, 1481, 1511, 1531, 1571, 1601, 1621, 1721, 1741, 1801, 1811, 1831, 1861, 1871, 1901, 1931, 1951, 10061, 10091, 10111, 10141
Offset: 1

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Comments

Complement of A208261 (nonprime numbers with all divisors starting and ending with digit 1) with respect to A208262 (numbers with all divisors starting and ending with digit 1). - Jaroslav Krizek, Mar 04 2012
Intersection of A030430 and A045707. - Michel Marcus, Jun 08 2013

Examples

			102701 is a member as it is a prime and the first and the last digits are both 1.

Links

Crossrefs

Cf. A208259 (Numbers starting and ending with digit 1).
Cf. A010051, A017281, A131835, A000030.

Programs

  • Haskell
    a062332 n = a062332_list !! (n-1)
a062332_list = filter ((== 1) . a010051') a208259_list
-- Reinhard Zumkeller, Jul 16 2014
  • Mathematica
    fl1Q[n_]:=Module[{idn=IntegerDigits[n]},First[idn]==Last[idn]==1]; Select[ Prime[Range[1300]],fl1Q] (* Harvey P. Dale, Apr 30 2012 *)
  • PARI
    { n=-1; t=log(10); forprime (p=2, 5*10^5, if ((p-10*(p\10)) == 1 && (p\10^(log(p)\t)) == 1, write("b062332.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Formula

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

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 29 2001
Missing term a(36)=1901 added by Harry J. Smith, Aug 05 2009

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 *)
Showing 1-3 of 3 results.

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

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