A104290 a = a(n) is such that the a-th prime p(a) is the least prime with digital sum equal to n, or a(n)=0 if no such prime exists.

0, 1, 2, 6, 3, 0, 4, 7, 0, 8, 10, 0, 19, 17, 0, 22, 24, 0, 46, 77, 0, 95, 109, 0, 168, 290, 0, 303, 430, 0, 669, 887, 0, 2064, 1117, 0, 3245, 4203, 0, 5133, 6057, 0, 7837, 9505, 0, 17984, 33067, 0, 49025, 49098, 0, 63951, 77777, 0, 216751, 216816, 0, 348513

Offset

1,3

Comments

a(1)=0 because there is no prime with digital sum equal to 1, a(2)=1 because p(1)=2 is the least prime with digital sum equal to 2, a(3)=2 because p(2)=3 the only prime with digital sum equal to 3, a(3k>3)=0 because there is no prime with digital sum equal to 3 (besides p(2)=3), a(53)=77777 because p(77777)=989999 is the least prime with digital sum (9+8+9+9+9+9) equal to 53. For the first 1,000,000 primes, the maximal digital sum is 62 (for p(658445)=9899999).

Links

Table of n, a(n) for n=1..58.

Mathematica

ta=Table[Plus@@IntegerDigits[Prime[i]], {i, 1000000}]; A104290={0, 1, 2, Table[If[Mod[k, 3]==0, 0, Position[ta, k][[1]]], {k, 4, 54}]}//Flatten

Crossrefs

Sequence in context: A102068 A351709 A188733 * A152549 A136759 A056129

Adjacent sequences: A104287 A104288 A104289 * A104291 A104292 A104293

Keyword

nonn,base

Author

Zak Seidov, Feb 28 2005

Status

approved