A222227 -id:A222227 - cp's OEIS frontend

A221211 Numbers n such that n and n + 4 are prime and there is a power of two in the interval (n,n+4).

3, 7, 13, 127

Offset: 1

Brad Clardy, Feb 21 2013

nonn

It is a conjecture that this is a finite sequence. These may be the only known cousin primes with this property.

The Cf.s list similar sequences, of the form -- numbers n such that n and n+m are prime and contain a power of two in the interval (n,n+m). The case where m=2, the twin prime case -- not listed, has only one member n=3. Another member would have to be a twin where n+2 was a Fermat type prime and n a Mersenne prime.

Cf. A023200.

Cf. A220951 (gap of 6), A213210 (8), A220746 (10), A213677 (12), A222424 (14), A222227 (16), A222219 (18).

//Program finds primes separated by an even number (called gap) which
//have a power of two between them. The program starts with the smallest
//of two above gap. Primes less than this starting point can be checked by
//inspection. In this example 3 also works.
gap:=4;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
    powerof2:=2^i;
    for k:=powerof2-gap+1 to powerof2-1 by 2 do
        if (IsPrime(k) and IsPrime(k+gap)) then k;
        end if;
    end for;
end for;

[n: n in PrimesUpTo(10^3) | IsPrime(n+4) and exists{t: t in [n+1..n+3 by 2] | IsOne(t/2^Valuation(t,2))}]; // Bruno Berselli, May 16 2013

A035044 Exchange 2 and 3.

Original entry on oeis.org

0, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 12, 14, 15, 16, 17, 18, 19, 30, 31, 33, 32, 34, 35, 36, 37, 38, 39, 20, 21, 23, 22, 24, 25, 26, 27, 28, 29, 40, 41, 43, 42, 44, 45, 46, 47, 48, 49, 50, 51, 53, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 62, 64, 65, 66, 67, 68

Offset: 0

N. J. A. Sloane

The map which is applied to primes in A171018. - M. F. Hasler, Feb 12 2013

Rearrangement of A001477 (the nonnegative integers). - Zak Seidov, Feb 15 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A001477, A171018, A222210-A222254; A171013-A171016, A175770.

FromDigits[IntegerDigits[#]/.{2->3,3->2}]&/@Range[0,68] (* Zak Seidov, Feb 15 2013 *)

A222227(n, d=[0, 1, 3, 2, 4, 5, 6, 7, 8, 9])=sum(i=1, #n=digits(n), d[n[i]+1]*10^(#n-i)) \\ gives correct value for n=0 iff d[1]=0, since digits(0)=[] in PARI (v.2.6), M. F. Hasler, Feb 12 2013

cp's OEIS Frontend

A221211 Numbers n such that n and n + 4 are prime and there is a power of two in the interval (n,n+4).

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