A065832 Numbers k such that the first k binary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).

2, 4, 10, 24, 29, 34, 43, 62, 76, 351, 778, 2736, 4992, 7517, 22044, 40390, 204505

Offset: 1

Author

Patrick De Geest, Nov 24 2001

Keywords

• nonn
• base
• hard
• more

Comments

In other words, take the decimal expansion of Pi, drop any digits greater than 1, omit the decimal point and look for prefixes in the resulting string which form base-2 primes.

Numbers k such that A065830(k) is prime.

Examples

			The first a(3)=10 binary digits of Pi are 1101110001_2 which is prime 881_10.
		

Crossrefs

Cf. A065828 up to A065840, A000796, A011545, A011546, A055143, A005042, A060421, A039954, A048796.

Programs

Mathematica

p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 2]], Print[n]], {n, 1, Length[p] } ]

Extensions

More terms from Robert G. Wilson v, Nov 30 2001

a(15)-a(16) from Chai Wah Wu, Apr 06 2020

a(17) from Michael S. Branicky, Sep 25 2024