A058938 Numbers k such that the sum of the first k digits of the decimal expansion of Pi is prime.

1, 6, 8, 13, 20, 21, 34, 36, 48, 56, 63, 87, 89, 92, 94, 104, 106, 107, 111, 116, 117, 118, 120, 130, 132, 133, 141, 146, 147, 162, 170, 173, 179, 183, 185, 186, 198, 202, 203, 206, 215, 217, 219, 220, 225, 242, 248, 249, 258, 264, 265, 270, 271, 285, 290, 291

Offset: 1

Author

G. L. Honaker, Jr., Jan 11 2001

Keywords

• easy
• nonn
• base

Examples

			6 is a term because 3 + 1 + 4 + 1 + 5 + 9 = 23, which is prime.
		

Crossrefs

Cf. A000796, A071117, A133213.

Programs

Maple

Digits := 2000: it := evalf(Pi, 2000): for i from 1 to 2000 do a[i] := floor(it): it := 10*(it-floor(it)): od: s := 0: for i from 1 to 2000 do s := s+a[i]: if isprime(s) then printf(`%d,`,i) fi: od:

Mathematica

a = First[ RealDigits[ N[ Pi, 300]]]; Do[ If[ PrimeQ[Plus @@ Take[a, n]], Print[n]], {n, 1, 300}]
Flatten[Position[Accumulate[RealDigits[\[Pi],10,500][[1]]], ?PrimeQ]]  (* _Harvey P. Dale, Apr 03 2011 *)

Extensions

More terms from James Sellers, Jan 14 2001