

A171667


Lesser of a pair of twin primes (p,p+2) sandwiched between two numbers (p1,p+3) having the same number of divisors.


4



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
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OFFSET

1,1


LINKS



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[p1]==f[p+3], AppendTo[lst, p]], {n, 7!}]; lst
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 *)


PROG

(PARI) forprime(p=o=0, 1e4, (2+o==o=p)&&numdiv(p3)==numdiv(p+1)&&print1(p2", ")) \\ M. F. Hasler, Jul 31 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



