cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A193238 Number of prime digits in decimal representation of n.

Original entry on oeis.org

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

Views

Author

Reinhard Zumkeller, Jul 19 2011

Keywords

Links

Crossrefs

Cf. A010051.
Cf. A211681, A046034, A052382, A055640, A055641, A055642, A102669 - A102685, A122640, A117804, A196563, A196564.

Programs

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)

A118950 Numbers containing at least one prime digit.

Original entry on oeis.org

2, 3, 5, 7, 12, 13, 15, 17, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 45, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 65, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 112
Offset: 1

Views

Author

Rick L. Shepherd, May 06 2006

Keywords

Comments

A193238(a(n)) > 0; complement of A084984; A092620, A092624 and A092625 are subsequences. - Reinhard Zumkeller, Jul 19 2011

Links

Crossrefs

Cf. A118951, A092620, A084984, A011540, A011531, A046034, A179336 (primes).

Programs

  • Haskell
    a118950 n = a118950_list !! (n-1)
a118950_list = filter (any (`elem` "2357") . show ) [0..]
-- Reinhard Zumkeller, Jul 19 2011
  • Mathematica
    Select[Range[150],AnyTrue[IntegerDigits[#],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 19 2018 *)
  • PARI
    is(n)=!!#select(isprime, digits(n)) \\ Charles R Greathouse IV, Sep 15 2015

Formula

a(n) = n + O(n^k) with k = log 6/log 10 = 0.77815.... - Charles R Greathouse IV, Sep 15 2015

A092620 Numbers with exactly one prime digit.

Original entry on oeis.org

2, 3, 5, 7, 12, 13, 15, 17, 20, 21, 24, 26, 28, 29, 30, 31, 34, 36, 38, 39, 42, 43, 45, 47, 50, 51, 54, 56, 58, 59, 62, 63, 65, 67, 70, 71, 74, 76, 78, 79, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 112, 113, 115, 117, 120, 121, 124, 126, 128, 129, 130, 131, 134
Offset: 1

Views

Author

Jani Melik, Apr 11 2004

Keywords

Comments

A193238(a(n))=1; subsequence of A118950. - Reinhard Zumkeller, Jul 19 2011

Examples

			12 has one prime digit, 2;
102 has one prime digit, 2.

Links

Crossrefs

Subsequence of A118950.
Cf. A046034, A084984, A092624, A092625.

Programs

  • Haskell
    import Data.List (elemIndices)
a092620 n = a092620_list !! (n-1)
a092620_list = elemIndices 1 a193238_list
-- Reinhard Zumkeller, Jul 19 2011
  • Maple
    stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr_n:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( isprime(i)='true' and ts_stpf(i) =0) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_n(300);
  • Mathematica
    Select[Range[150],Count[IntegerDigits[#],?(PrimeQ)]==1&] (* _Harvey P. Dale, Mar 23 2018 *)

Formula

There are 6^n*(n-1/6)*2/3 n-digit members of this sequence for n > 1. - Charles R Greathouse IV, Apr 23 2022

A092625 Numbers with exactly three prime digits.

Original entry on oeis.org

222, 223, 225, 227, 232, 233, 235, 237, 252, 253, 255, 257, 272, 273, 275, 277, 322, 323, 325, 327, 332, 333, 335, 337, 352, 353, 355, 357, 372, 373, 375, 377, 522, 523, 525, 527, 532, 533, 535, 537, 552, 553, 555, 557, 572, 573, 575, 577, 722, 723, 725
Offset: 1

Views

Author

Jani Melik, Apr 11 2004

Keywords

Comments

It is the same as A046034 from two digit numbers from 22 up to four digit numbers from 1222.
A193238(a(n))=3; subsequence of A118950. [Reinhard Zumkeller, Jul 19 2011]

Examples

			222 has three prime digits, three times 2;
1235 has three prime digits, 2, 3 and 5.

Links

Crossrefs

Cf. A034895, A046034, A085557, A019546, A034844.
Cf. A084984, A092620, A092624.

Programs

  • Haskell
    import Data.List (elemIndices)
a092625 n = a092625_list !! (n-1)
a092625_list = elemIndices 3 a193238_list
-- Reinhard Zumkeller, Jul 19 2011
  • Maple
    stev_sez:=proc(n) local i, tren, st, ans, anstren; ans:=[ ]: anstren:=[ ]: tren:=n: for i while (tren>0) do st:=round( 10*frac(tren/10) ): ans:=[ op(ans), st ]: tren:=trunc(tren/10): end do; for i from nops(ans) to 1 by -1 do anstren:=[ op(anstren), op(i,ans) ]; od; RETURN(anstren); end: ts_stpf:=proc(n) local i, stpf, ans; ans:=stev_sez(n): stpf:=0: for i from 1 to nops(ans) do if (isprime(op(i,ans))='true') then stpf:=stpf+1; # number of prime digits fi od; RETURN(stpf) end: ts_pr_nt:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( ts_stpf(i) = 3) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_nt(2000);
  • Mathematica
    Select[Range[800],Total[Boole[PrimeQ[IntegerDigits[#]]]]==3&] (* Harvey P. Dale, Dec 31 2023 *)
Showing 1-4 of 4 results.

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