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

1,1

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,....

Links

Table of n, a(n) for n=1..87.

Example

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.

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

Crossrefs

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

Sequence in context: A251844 A237230 A206516 * A014895 A106300 A252601

Adjacent sequences: A119374 A119375 A119376 * A119378 A119379 A119380

Keyword

base,nonn

Author

Robert G. Wilson v, Jul 24 2006

Status

approved