A193238 -id:A193238 - cp's OEIS frontend

A092624 Numbers with exactly two prime digits.

22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 122, 123, 125, 127, 132, 133, 135, 137, 152, 153, 155, 157, 172, 173, 175, 177, 202, 203, 205, 207, 212, 213, 215, 217, 220, 221, 224, 226, 228, 229, 230, 231, 234, 236, 238, 239, 242, 243, 245

Offset: 1

Jani Melik, Apr 11 2004

A193238(a(n))=2; subsequence of A118950. [Reinhard Zumkeller, Jul 19 2011]

			25 has two prime digits, 2 and 5;
207 has two prime digits, 2 and 7.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A034895, A046034, A085557, A019546, A034844.

Cf. A084984, A092620, A092625.

import Data.List (elemIndices)
a092624 n = a092624_list !! (n-1)
a092624_list = elemIndices 2 a193238_list
-- Reinhard Zumkeller, Jul 19 2011

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_nd:=proc(n) local i, stpf, ans, ans1, tren; ans:=[ ]: stpf:=0: tren:=1: for i from 1 to n do if ( ts_stpf(i) = 2) then ans:=[ op(ans), i ]: tren:=tren+1; fi od; RETURN(ans) end: ts_pr_nd(500);

Select[Range[300],Count[IntegerDigits[#],?PrimeQ]==2&] (* _Harvey P. Dale, Apr 20 2025 *)

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

Jani Melik, Apr 11 2004

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]

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A034895, A046034, A085557, A019546, A034844.

Cf. A084984, A092620, A092624.

import Data.List (elemIndices)
a092625 n = a092625_list !! (n-1)
a092625_list = elemIndices 3 a193238_list
-- Reinhard Zumkeller, Jul 19 2011

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);

Select[Range[800],Total[Boole[PrimeQ[IntegerDigits[#]]]]==3&] (* Harvey P. Dale, Dec 31 2023 *)

A179335 a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).

Original entry on oeis.org

2, 3, 5, 7, 11, 3, 7, 19, 2, 2, 3, 3, 41, 3, 7, 3, 5, 61, 7, 7, 3, 7, 3, 89, 7, 101, 3, 7, 109, 3, 2, 3, 3, 3, 149, 5, 5, 3, 7, 3, 7, 181, 19, 3, 7, 19, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 401, 409, 19, 2, 3, 3, 3, 3, 449, 5, 61, 3, 7, 7, 7

Offset: 1

Reinhard Zumkeller, Jul 11 2010

a(n) < 10 iff prime(n) is in A179336;

a(n) = prime(n) iff prime(n) is in A033274. [Corrected by M. F. Hasler, Aug 27 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A070024, A019546, A092629, A104250, A019546, A034844, A179336, A193238.

A179335(n)={my(p=prime(n),m=0,M); for(d=1,n, M=10^d; n=p; until(n<=M || !n\=10, isprime(n%M) & (!m || m>n%M) & m=n%M); m & return(m))} \\ M. F. Hasler, Aug 27 2012

from sympy import isprime, prime
def a(n):
    s = str(prime(n))
    ss = set(int(s[i:i+1+l]) for i in range(len(s)) for l in range(len(s)))
    return min(t for t in ss if isprime(t))
print([a(n) for n in range(1, 94)]) # Michael S. Branicky, Jun 29 2022

A276729 Number of nonprime digits in the decimal expansion of n.

Original entry on oeis.org

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

Offset: 0

M. F. Hasler, Sep 16 2016

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A055642, A193238, A085557, A046034 (indices of 0's), A084984, A085558, A202267, A202268.

Cf. A011557 (integers that give records).

f:= proc(n) local t; option remember;
  t:= n mod 10;
procname((n-t)/10) + `if`(member(t,[2,3,5,7]),0,1)
end proc:
f(0):= 0:
1,seq(f(i),i=1..100); # Robert Israel, Feb 27 2019

PARI
```
a(n)=#select(t->!isprime(t),digits(n))
```

a(n) = A055642(n) - A193238(n).

a(A046034(n)) = 0. - Gordon Atkinson, Sep 06 2019

A257629 Duplicate of A276729.

Original entry on oeis.org

1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 3

Offset: 0

Giovanni Teofilatto, Jul 12 2015

dead

			a(10344) = 4 because 4 of the digits of 10344 (1, 0, 4 and 4) are nonprime.

Cf. A055642 (number of digits), A193238 (number of prime digits), A046034.

a[n_] := Length@ Intersection[ IntegerDigits[n], {0, 1, 4, 6, 8, 9}]; a/@ Range[0, 90] (* Giovanni Resta, Jul 14 2015 *)
Table[Count[IntegerDigits[n],?(!PrimeQ[#]&)],{n,0,100}] (* _Harvey P. Dale, Jan 16 2017 *)

a(n) = A055642(n) - A193238(n). - Michel Marcus, Jul 14 2015

Corrected and extended by Giovanni Resta, Jul 14 2015

Corrected and extended by Harvey P. Dale, Jan 16 2017

cp's OEIS Frontend

A092624 Numbers with exactly two prime digits.

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A092625 Numbers with exactly three prime digits.

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A179335 a(n) is the smallest prime which appears as a substring of the decimal representation of prime(n).

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A276729 Number of nonprime digits in the decimal expansion of n.

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A257629 Duplicate of A276729.

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