A084984 -id:A084984 - 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 *)

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

A085558 Numbers that have more nonprime digits than prime digits.

Original entry on oeis.org

0, 1, 4, 6, 8, 9, 10, 11, 14, 16, 18, 19, 40, 41, 44, 46, 48, 49, 60, 61, 64, 66, 68, 69, 80, 81, 84, 86, 88, 89, 90, 91, 94, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 124, 126, 128, 129, 130

Offset: 1

Jason Earls, Jul 04 2003

Cf. A084984.

pdnpdQ[n_]:=With[{idn=IntegerDigits[n]},Count[idn,?(PrimeQ[#]&)]<Count[idn,?(!PrimeQ[ #]&)]]; Select[Range[0,150],pdnpdQ] (* Harvey P. Dale, Dec 19 2023 *)

isok(n) = {my(d = if (n, digits(n), [0]), nbp = #select(x->isprime(x), d)); 2*nbp < #d;} \\ Michel Marcus, Feb 28 2019

0 added by Arkadiusz Wesolowski, Jul 11 2011

A084988 Numbers made with nonprime digits such that the sum of the digits is also not prime.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 18, 19, 40, 44, 46, 48, 60, 64, 66, 68, 69, 80, 81, 84, 86, 88, 90, 91, 96, 99, 100, 108, 109, 114, 116, 118, 141, 144, 149, 161, 168, 169, 180, 181, 186, 189, 190, 194, 196, 198

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003

			E.g. 46 is not prime and 4+6 =10 is also not prime.

Harvey P. Dale, Table of n, a(n) for n = 1..5000

Cf. A084984.

Select[Rest[FromDigits/@Tuples[{0,1,4,6,8,9},3]],!PrimeQ[ Total[ IntegerDigits[ #]]]&] (* Harvey P. Dale, Jul 20 2017 *)

A155547 a(n) = prime(n) without prime digits in n.

Original entry on oeis.org

2, 7, 13, 19, 23, 29, 31, 43, 53, 61, 67, 173, 179, 193, 199, 223, 227, 281, 283, 311, 317, 337, 347, 409, 419, 433, 443, 457, 461, 463, 467, 491, 503, 521, 523, 541, 547, 569, 577, 593, 599, 601, 607, 619, 641, 647, 653, 809, 811, 827, 839, 857, 859, 941, 947

Offset: 1

Juri-Stepan Gerasimov, Jan 24 2009

Prime digit = 2, 3, 5 or 7.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000027, A000040.

isA084984 := proc(n) local dgs ; dgs := convert(convert(n,base,10),set) ; if dgs intersect {2,3,5,7} <> {} then false; else true; fi; end: A084984 := proc(n) option remember ; local a ; if n = 1 then 1; else for a from procname(n-1)+1 do if isA084984(a) then RETURN(a) ; fi; od; fi; end: A155547 := proc(n) ithprime(A084984(n)) ; end: for n from 1 to 80 do printf("%d,",A155547(n)) ; od: # R. J. Mathar, Jan 25 2009

Prime[#]&/@Select[Range[200],NoneTrue[IntegerDigits[#],PrimeQ]&] (* Harvey P. Dale, Jan 28 2024 *)

a(n) = A000040(A084984(n)). - R. J. Mathar, Jan 25 2009

A365471 Numbers whose digits are not all primes.

Original entry on oeis.org

0, 1, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 26, 28, 29, 30, 31, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 74, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

James C. McMahon, Sep 11 2023

Complement of A046034.

Union of A084984 and A365589.

Cf. A046034, A084984, A365589.

a[n_Integer?NonNegative] := Select[Range[0, n], Not[AllTrue[MemberQ[{2, 3, 5, 7}, #] & /@ IntegerDigits@#, Identity]] &]; a[86] (* Robert P. P. McKone, Sep 13 2023 *)
Select[Range[0,100],AnyTrue[IntegerDigits[#],!PrimeQ[#]&]&] (* Harvey P. Dale, Dec 22 2023 *)

A365472 Numbers whose digits are either all primes or all nonprimes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 16, 18, 19, 22, 23, 25, 27, 32, 33, 35, 37, 40, 41, 44, 46, 48, 49, 52, 53, 55, 57, 60, 61, 64, 66, 68, 69, 72, 73, 75, 77, 80, 81, 84, 86, 88, 89, 90, 91, 94, 96, 98, 99, 100, 101, 104, 106, 108, 109, 110, 111, 114

Offset: 1

James C. McMahon, Sep 11 2023

Complement of A365589.

Union of A046034 and A084984.

Cf. A046034, A084984, A365589.

a[n_Integer?NonNegative] := Select[Range[0, n], Module[{digits, primeDigits}, digits = IntegerDigits[#]; primeDigits = MemberQ[{2, 3, 5, 7}, #] & /@ digits; AllTrue[primeDigits, Identity] || AllTrue[primeDigits, Not]] &]; a[114] (* Robert P. P. McKone, Sep 13 2023 *)

A380490 Replace prime digits of n by 0's.

Original entry on oeis.org

1, 0, 0, 4, 0, 6, 0, 8, 9, 10, 11, 10, 10, 14, 10, 16, 10, 18, 19, 0, 1, 0, 0, 4, 0, 6, 0, 8, 9, 0, 1, 0, 0, 4, 0, 6, 0, 8, 9, 40, 41, 40, 40, 44, 40, 46, 40, 48, 49, 0, 1, 0, 0, 4, 0, 6, 0, 8, 9, 60, 61, 60, 60, 64, 60, 66, 60, 68, 69, 0, 1, 0, 0, 4, 0, 6, 0, 8, 9, 80, 81, 80

Offset: 1

Ctibor O. Zizka, Jan 25 2025

			n = 7: 7 --> 0, thus a(7) = 0.
n = 26: 26 --> 06, thus a(26) = 6.
n = 472: 472 --> 400, thus a(472) = 400.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A046034, A084984.

f:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(`if`(isprime(L[i]),0,L[i]) * 10^(i-1),i=1..nops(L))
end proc:
map(f, [$1..100]); # Robert Israel, May 18 2025

a[n_] := FromDigits[IntegerDigits[n] /. ?PrimeQ -> 0]; Array[a, 100] (* _Amiram Eldar, Jan 25 2025 *)

def a(n): return int(str(n).translate({50:48,51:48,53:48,55:48}))
print([a(n) for n in range(1, 83)]) # Michael S. Branicky, Jan 25 2025

a(A084984(n)) = A084984(n).

a(A046034(n)) = 0.

A383934 Composite numbers that contain only nonprime digits and whose prime factors contain only nonprime digits.

Original entry on oeis.org

1111, 1199, 1681, 1691, 1919, 1991, 4141, 4411, 4469, 4499, 4609, 4961, 6109, 6161, 6611, 6649, 6809, 8899, 8989, 9089, 9481, 9691, 10109, 10901, 11009, 11041, 11099, 11419, 11881, 14641, 14801, 16109, 16441, 16489, 16999, 18409, 18491, 18601, 18689

Offset: 1

Scott R. Shannon, Aug 17 2025

			10109 is a term as 10109 = 11 * 919, and both the number and its prime factors only contain nonprime digits.

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Cf. A084984, A018252, A387093, A000040.

Select[Select[Range[20000], And[CompositeQ[#], NoneTrue[IntegerDigits[#], PrimeQ]] &], NoneTrue[Flatten[IntegerDigits /@ FactorInteger[#][[All, 1]] ], PrimeQ] &] (* Michael De Vlieger, Aug 23 2025 *)

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

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A085558 Numbers that have more nonprime digits than prime digits.

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A084988 Numbers made with nonprime digits such that the sum of the digits is also not prime.

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A155547 a(n) = prime(n) without prime digits in n.

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A365471 Numbers whose digits are not all primes.

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Mathematica

A365472 Numbers whose digits are either all primes or all nonprimes.

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