A065840 Numbers n such that the first n quaternary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).

1, 2, 3, 5, 10, 19, 72, 115, 220, 315, 375, 12408

Offset: 1

Author

Patrick De Geest, Nov 24 2001

Keywords

• nonn
• base
• hard

Comments

In other words, take the decimal expansion of Pi, drop any digits greater than 4, omit the decimal point and look for prefixes in the resulting string which form base-4 primes.

Numbers n such that A065838(n) is prime.

The next term in the sequence, if it exists, is greater than 10000. - Nathaniel Johnston, Nov 15 2010

Examples

			E.g., the first a(5) or 10 quaternary digits of Pi are 31.12332323{4} and 3112332323{4} is the prime 880571{10}.
		

Crossrefs

Cf. A065828 up to A065839, A000796, A011545, A011546, A055145, A005042, A060421, A039954, A048796.

Programs

Mathematica

p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]

Extensions

a(12) from Chai Wah Wu, Apr 07 2020