A065840 - OEIS

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

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OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

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

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} ]

CROSSREFS

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

Sequence in context: A365858 A007569 A054317 * A181934 A093785 A105369

Adjacent sequences: A065837 A065838 A065839 * A065841 A065842 A065843

KEYWORD

nonn,base,hard

AUTHOR

Patrick De Geest, Nov 24 2001

EXTENSIONS

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

STATUS

approved