The On-Line Encyclopedia of Integer Sequences (OEIS)

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A171667

Lesser of a pair of twin primes (p,p+2) sandwiched between two numbers (p-1,p+3) having the same number of divisors.
(history; published version)

#8 by Harvey P. Dale at Thu Jul 04 18:27:22 EDT 2019

STATUS

editing

approved

#7 by Harvey P. Dale at Thu Jul 04 18:27:18 EDT 2019

LINKS

Harvey P. Dale, <a href="/A171667/b171667.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#6 by Harvey P. Dale at Thu Jul 04 18:25:31 EDT 2019

STATUS

editing

approved

#5 by Harvey P. Dale at Thu Jul 04 18:25:28 EDT 2019

MATHEMATICA

Select[Range[11000], DivisorSigma[0, #-1]==DivisorSigma[0, #+3]&&AllTrue[{#, #+2}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 04 2019 *)

STATUS

approved

editing

#4 by M. F. Hasler at Fri Jul 31 15:04:23 EDT 2015

STATUS

editing

approved

#3 by M. F. Hasler at Fri Jul 31 15:03:13 EDT 2015

NAME

Lesser of a pair of twin primes; Twin Primes (p,p+2) sandwiched between two numbers (p-1,p+3) having the same number of divisors.

PROG

(PARI) forprime(p=o=0, 1e4, (2+o==o=p)&&numdiv(p-3)==numdiv(p+1)&&print1(p-2", ")) \\ M. F. Hasler, Jul 31 2015

EXTENSIONS

Name edited by M. F. Hasler, Jul 31 2015

STATUS

approved

editing

#2 by Russ Cox at Sat Mar 31 12:38:28 EDT 2012

AUTHOR

_Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), _, Dec 14 2009

Discussion

Sat Mar 31

12:38

OEIS Server: https://oeis.org/edit/global/876

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Lesser of twin primes; Twin Primes sandwiched between two numbers having the same number of divisors.

DATA

11, 29, 59, 431, 599, 827, 1031, 1319, 1619, 1787, 2111, 2141, 2267, 2687, 2711, 3299, 3329, 3371, 3527, 3671, 4001, 4091, 4229, 4259, 5021, 5099, 5519, 5867, 6299, 6659, 6779, 7331, 7457, 8087, 8231, 8387, 8627, 8861, 8999, 9419, 9461, 9767, 10139

OFFSET

1,1

EXAMPLE

First term 11: 10={1,2,5,10},14={1,2,7,14} Second term 29: 28={1,2,4,7,14,28},32={1,2,4,8,16,32}

MATHEMATICA

f[n_]:=Length[Divisors[n]]; lst={}; Do[p=Prime[n]; If[PrimeQ[p+2]&&f[p-1]==f[p+3], AppendTo[lst, p]], {n, 7!}]; lst

CROSSREFS

Cf. A005237, A067889

KEYWORD

nonn

AUTHOR

Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 14 2009

STATUS

approved