A091020 Numbers n such that in binary representation n is a substring of the n-th prime.

1, 5, 6, 15, 31, 32, 34, 39, 49, 50, 81, 82, 1052, 1799, 2119, 2573, 3378, 3447, 52225, 61870, 95752, 186157, 213547, 644695, 750550, 1414920, 2034869, 3768375, 4189897, 24628414, 50359121, 74288549, 87706569, 87706570

Offset: 1

Author

Reinhard Zumkeller, Dec 14 2003

Keywords

• nonn
• base

Comments

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

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

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..62 (terms < 10^12)
• Re: 2^k - prime(p) or prime(p) - 2^k ?, SeqFan mailing list, Apr 10 2013

Crossrefs

Cf. A004676, A007088, A221860.

Programs

Mathematica

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 *)

Formula

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

Extensions

a(22)-a(34) from Donovan Johnson, May 08 2012