A091020 - OEIS

%I #26 Dec 23 2024 14:53:42

%S 1,5,6,15,31,32,34,39,49,50,81,82,1052,1799,2119,2573,3378,3447,52225,

%T 61870,95752,186157,213547,644695,750550,1414920,2034869,3768375,

%U 4189897,24628414,50359121,74288549,87706569,87706570

%N Numbers n such that in binary representation n is a substring of the n-th prime.

%C A007088(a(n)) is a substring of A004676(a(n)).

%C The terms of A221860 \ {2,3} form a subsequence of this sequence.

%H Giovanni Resta, <a href="/A091020/b091020.txt">Table of n, a(n) for n = 1..62</a> (terms < 10^12)

%H <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-April/011029.html">Re: 2^k - prime(p) or prime(p) - 2^k ?</a>, SeqFan mailing list, Apr 10 2013

%F a(n) = A049084(A091021(n)), A000040(a(n)) = A091021(n).

%e A000040(50) = 229: 50->110010, 229->11100101 = 1'110010'1, therefore 50 is a term.

%e prime(4189897) = 100001111111110111011001001[2] = 2^26 + 4189897. Apart from p=2 and p=3, this is the only prime below primepi(10^8) such that prime(p)-p = 2^k. See A221860 for further examples. - _M. F. Hasler_, Apr 10 2013

%t Select[Range[800000],SequenceCount[IntegerDigits[Prime[#],2],IntegerDigits[#,2]]>0&] (* The program generates the first 25 terms of the sequence. *) (* _Harvey P. Dale_, Nov 04 2024 *)

%Y Cf. A004676, A007088, A221860.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, Dec 14 2003

%E a(22)-a(34) from _Donovan Johnson_, May 08 2012