A119377 Numbers k such that the next k binary digits of Pi are odd primes with no leading zeros.

2787, 6, 7, 23, 2, 3, 3, 8, 2, 2, 2, 5, 8, 2, 18, 9, 10, 413, 8, 3, 2, 4019, 14, 4, 2, 2, 11, 21, 4, 2, 3, 6, 2, 11, 3, 5, 19, 2, 6, 2, 4, 32, 2, 56, 31, 6, 7, 7, 2, 32, 20, 9, 10, 900, 2, 2, 2, 97, 5, 2, 8, 64, 3, 13, 3, 2, 6, 7, 15, 3, 2666, 7, 8, 3, 14, 3, 2, 2, 6, 5, 92, 17, 31, 4, 241, 78, 3

Offset: 1

Author

Robert G. Wilson v, Jul 24 2006

Keywords

• base
• nonn

Comments

Partition the string of binary digits of Pi in such a way that each partition begins and ends with 1 (thus no leading or trailing zeros) and each such partition is prime.

Pi_2 = 1100100100001111110110101010001000100001011010001100001000..._2 (A004601).

If 2 is allowed as a member, then the sequence begins: 2787,2,5,6,2,2,2,39,5,8,2,18,9,10,2,153,2,6,2,18,7,7,12,2,2,2,2,....

Examples

			a(1) represents the binary number 1100100100...(2767 terms)...0100000011 which equals the decimal number 7339860347...(819 terms)...8308318467 which is a prime.
a(2) represents the binary number 101001 which equals the decimal number 41, a prime.
		

Crossrefs

Cf. A004601, A068425, A117721, A065987, A119017.

Programs

Mathematica

ps = First@ RealDigits[Pi, 2, 12010]; lst = {}; Do[k = 1; While[fd = FromDigits[ Take[ps, k], 2]; EvenQ@fd || ps[[k + 1]] == 0 || !PrimeQ@fd, k++ ]; AppendTo[lst, k]; ps = Drop[ps, k], {n, 87}]; lst