A062332 Primes starting and ending with 1.

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

Author

Amarnath Murthy, Jun 21 2001

Keywords

• nonn
• base
• easy

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

• Harry J. Smith, Table of n, a(n) for n = 1..1000

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