A091021 Primes p=prime(k) such that in binary representation k is a substring of p.

2, 11, 13, 47, 127, 131, 139, 167, 227, 229, 419, 421, 8419, 15391, 18503, 23053, 31333, 32119, 642049, 771769, 1240081, 2545453, 2951341, 9677999, 11390809, 22436899, 33056171, 63701437, 71298761, 465462769, 989883217, 1490754379, 1775394377, 1775394389

Offset: 1

Author

Reinhard Zumkeller, Dec 14 2003

Keywords

• nonn
• base

Examples

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

Crossrefs

Cf. A007088, A004676.

Programs

Python

from sympy import primerange
[print(i, end=', ') for n, i in enumerate(primerange(1, 10**7)) if bin(n+1)[2:] in bin(i)[2:]]; # Nicholas Stefan Georgescu, Jan 03 2025

Formula

a(n) = A000040(A091020(n)).

A091020(n) = A049084(a(n)).

Extensions

a(22)-a(32) from Donovan Johnson, May 03 2010

a(33)-a(34) from Donovan Johnson, May 08 2012