A193238 Number of prime digits in decimal representation of n.

0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1

Offset

0,23

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(A084984(n))=0; a(A118950(n))>0; a(A092620(n))=1; a(A092624(n))=2; a(A092625(n))=3; a(A046034(n))=A055642(A046034(n));

a(A000040(n)) = A109066(n).

From Hieronymus Fischer, May 30 2012: (Start)

a(n) = sum_{j=1..m+1} (floor(n/10^j+0.3) + floor(n/10^j+0.5) + floor(n/10^j+0.8) - floor(n/10^j+0.2) - floor(n/10^j+0.4) - floor(n/10^j+0.6)), where m=floor(log_10(n)), n>0.

a(10n+k) = a(n) + a(k), 0<=k<10, n>=0.

a(n) = a(floor(n/10)) + a(n mod 10), n>=0.

a(n) = sum_{j=0..m} a(floor(n/10^j) mod 10), n>=0.

a(A046034(n)) = floor(log_4(3n+1)), n>0.

a(A211681(n)) = 1 + floor((n-1)/4), n>0.

G.f.: g(x) = (1/(1-x))*sum_{j>=0} (x^(2*10^j) + x^(3*10^j)+ x^(5*10^j) + x^(7*10^j))*(1-x^10^j)/(1-x^10^(j+1)).

Also: g(x) = (1/(1-x))*sum_{j>=0} (x^(2*10^j)- x^(4*10^j)+ x^(5*10^j)- x^(6*10^j)+ x^(7*10^j)- x^(8*10^j))/(1-x^10^(j+1)). (End)

Mathematica

Count[IntegerDigits[#], _?PrimeQ]&/@Range[0, 100] (* Harvey P. Dale, Nov 13 2022 *)

Prog

(Haskell)
a193238 n = length $ filter (`elem` "2357") $ show n
(PARI) a(n)=n=eval(Vec(Str(n))); sum(i=1, #n, isprime(n[i])) \\ Charles R Greathouse IV, Jul 29 2011

Crossrefs

Cf. A010051.

Cf. A211681, A046034, A052382, A055640, A055641, A055642, A102669 - A102685, A122640, A117804, A196563, A196564.

Sequence in context: A138328 A137264 A289014 * A323826 A275824 A324869

Adjacent sequences: A193235 A193236 A193237 * A193239 A193240 A193241

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 19 2011

Status

approved