A232237 Primes p such that p-2 and q are primes, where q is concatenation of binary representations of p and p-2: q = p * 2^L + p-2, where L is the length of binary representation of p-2: L=A070939(p-2).

5, 7, 31, 271, 283, 433, 1291, 1321, 1429, 1489, 1951, 4723, 5503, 6091, 6133, 6553, 6871, 16651, 16981, 17029, 17191, 17209, 17749, 17791, 18541, 18919, 19471, 20149, 20479, 20551, 20809, 21319, 21649, 21739, 22111, 25309, 25801, 27061, 27409, 27541, 27691, 28549, 29131

Offset: 1

Author

Alex Ratushnyak, Nov 20 2013

Keywords

• nonn
• base
• less

Examples

			5 is 101 in binary, 3 is 11, and because 10111 = 23d is a prime, 5 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A070939, A232235.

Programs

Mathematica

Select[Partition[Prime[Range[3200]],2,1],#[[2]]-#[[1]]==2&&PrimeQ[ FromDigits[ Join[IntegerDigits[#[[2]],2],IntegerDigits[#[[1]],2]],2]]&][[All,2]] (* Harvey P. Dale, Feb 25 2018 *)

Formula

A232235(n) = a(n) * 2^A070939(a(n)-2) + a(n)-2.