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,....
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
KEYWORD
base,nonn
AUTHOR
Robert G. Wilson v, Jul 24 2006
STATUS
approved