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Number of lesser twin primes (A001359) in range ]2^n, 2^(n+1)].
3

%I #35 Feb 07 2024 09:12:06

%S 1,1,1,2,2,3,7,7,12,26,45,70,113,215,355,666,1153,2071,3785,6965,

%T 12495,22643,41608,76371,140944,261752,484968,904799,1689477,3160113,

%U 5928904,11139071,20970782,39535081,74697745,141342490,267812262,508194094,965623233,1837147717

%N Number of lesser twin primes (A001359) in range ]2^n, 2^(n+1)].

%C Conjecture: a(n) > 0 for all n. This holds for all n <= 100. - _Charles R Greathouse IV_, May 14 2012

%H Jerry M Lagrou, <a href="/A095017/b095017.txt">Table of n, a(n) for n = 1..47</a>

%H <a href="/index/Pri#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>

%t Table[ps = Prime[Range[PrimePi[2^n] + 1, PrimePi[2^(n+1) + 1]]]; Count[Differences[ps], 2], {n, 25}] (* _T. D. Noe_, May 08 2012 *)

%o (PARI) a095017(maxex2)={my (L=List([1]), p2=8, n2=0, pp=5); forprime (p=7, 2^maxex2, if (p>p2, p2*=2; listput(L,n2); n2=0); if (p-pp==2, n2++); pp=p); Vec(L)};

%o a095017(30) \\ _Hugo Pfoertner_, Feb 05 2024

%Y Cf. A033843, A095016, A036378.

%K nonn

%O 1,4

%A _Antti Karttunen_ and _Labos Elemer_, Jun 01 2004

%E a(34) and beyond from _Jerry M Lagrou_, Dec 02 2023