A107342 -id:A107342 - cp's OEIS frontend

A107666 Primes having only {4, 6, 9} as digits.

449, 499, 4649, 4969, 4999, 6449, 6469, 6949, 9649, 9949, 44449, 44699, 46499, 46649, 49499, 49669, 49999, 64499, 64969, 66449, 66499, 66949, 69499, 94649, 94949, 94999, 96469, 99469, 444449, 444469, 444649, 446969, 449699, 464699, 464999, 466649, 469649, 469969

Offset: 1

Rick L. Shepherd, May 19 2005

Intersection of A000040 and A107665. - K. D. Bajpai, Sep 08 2014

			From _K. D. Bajpai_, Sep 08 2014: (Start)
4649 is a term because it is a prime having only semiprime digits 4, 6 and 9.
6469 is a term because it is a prime having only semiprime digits 4, 6 and 9.
449 is the smallest prime comprising only semiprime digits 4, 6 or 9.
(End)

Jason Bard, Table of n, a(n) for n = 1..10000 (first 2069 terms from K. D. Bajpai)
Index to entries for primes with digits in a given set

Cf. A107665 (numbers with semiprime digits), A001358 (semiprimes), A051416 (primes whose digits are all composite), A020466 (primes with digits 4 and 9 only), A093402 (primes of form 44...9), A093945 (primes of form 499...).
Cf. A107342, A111494, A111496, A111697.
Cf. A385768 - A385800.

N:= 4:  Dgts:= {4, 6, 9}:  A:= NULL:
for d from 1 to N do
K:= combinat[cartprod]([Dgts minus {0}, Dgts $(d-1)]);
while not K[finished] do L:= K[nextvalue]();  x:= add(L[i]*10^(d-i), i=1..d);
if isprime(x) then A:= A, x fi od od: A;  # K. D. Bajpai, Sep 08 2014

Select[Prime[Range[50000]], Intersection[IntegerDigits[#], {0, 1, 2, 3, 5, 7, 8}] == {} &] (* K. D. Bajpai, Sep 08 2014 *)

a(35)-a(38) from K. D. Bajpai, Sep 08 2014

A107665 Numbers with semiprime digits (digits 4, 6, 9 only).

Original entry on oeis.org

4, 6, 9, 44, 46, 49, 64, 66, 69, 94, 96, 99, 444, 446, 449, 464, 466, 469, 494, 496, 499, 644, 646, 649, 664, 666, 669, 694, 696, 699, 944, 946, 949, 964, 966, 969, 994, 996, 999, 4444, 4446, 4449, 4464, 4466, 4469, 4494, 4496, 4499, 4644, 4646, 4649, 4664

Offset: 1

Rick L. Shepherd, May 19 2005

Cf. A107666 (primes in this sequence), A001358 (semiprimes), A029581 (all digits are composite).

Cf. A107342, A111494, A111496, A111697.

Select[Range[5000],Union[Pick[DigitCount[#],{1,1,1,0,1,0,1,1,0,1},1]] == {0}&] (* Harvey P. Dale, Oct 21 2011 *)
Flatten[Table[FromDigits/@Tuples[{4,6,9},n],{n,4}]] (* Harvey P. Dale, Oct 21 2014 *)

A111494 3-almost primes with semiprime digits (digits 4, 6, 9 only).

Original entry on oeis.org

44, 66, 99, 494, 646, 946, 964, 969, 994, 4646, 4669, 4949, 4966, 4994, 4996, 6446, 6466, 6494, 6946, 6964, 6969, 6994, 9494, 9499, 9644, 9669, 9694, 9699, 9994, 44446, 44466, 44644, 44666, 44994, 46446, 46466, 46646, 46669, 46694, 46699, 46949

Offset: 1

Jonathan Vos Post, Nov 15 2005

			a(1) = 44 = 2^2 * 11, a(2) = 66 = 2 * 3 * 11, a(3) = 99 = 3^2 * 11, a(4) = 494 = 2 * 13 * 19, a(5) = 646 = 2 * 17 * 19, a(6) = 946 = 2 * 11 * 43, a(7) = 964 = 2^2 * 241, a(8) = 969 = 3 * 17 * 19, a(9) = 994 = 2 * 7 * 71, a(10) = 4646 = 2 * 23 * 101, a(11) = 4669 = 7 * 23 * 29.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358, A014612, A107665, A107666, A107342, A111496, A111697.

Table[Select[FromDigits/@Tuples[{4,6,9},n],PrimeOmega[#]==3&],{n,5}]// Flatten (* Harvey P. Dale, Jan 08 2019 *)

do(N)=my(v=List(),a=[4,6,9]); for(d=1,N, forvec(u=vector(d,i,[1,3]), t=fromdigits(apply(n->a[n],u)); if(bigomega(t)==3, listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Corrected by Ray Chandler, Nov 19 2005

A111496 4-almost primes with semiprime digits (digits 4, 6, 9 only).

Original entry on oeis.org

444, 644, 664, 666, 966, 996, 999, 4444, 4466, 4494, 4696, 4964, 6644, 6666, 6699, 9444, 9496, 9646, 9964, 9966, 9999, 44444, 44499, 44646, 44996, 46444, 46449, 46964, 46996, 49444, 49494, 49946, 49966, 49996, 64446, 64494, 64644, 64666

Offset: 1

Jonathan Vos Post, Nov 16 2005

			a(1) = 444 = 2^2 * 3 * 37, a(2) = 644 = 2^2 * 7 * 23, a(3) = 664 = 2^3 * 83, a(4) = 666 = 2 * 3^2 * 37, a(5) = 966 = 2 * 3 * 7 * 23, a(6) = 996 = 2^2 * 3 * 83, a(7) = 999 = 3^3 * 37, a(8) = 4466 = 2 * 7 * 11 * 29, a(9) = 4494 = 2 * 3 * 7 * 107, a(10) = 4696 = 2^3 * 587.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358, A014613, A107665, A107666, A107342, A111494, A111697.

do(N)=my(v=List(), a=[4, 6, 9]); for(d=1, N, forvec(u=vector(d, i, [1, 3]), t=fromdigits(apply(n->a[n], u)); if(bigomega(t)==4, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

A111697 5-almost primes with semiprime digits (digits 4, 6, 9 only).

Original entry on oeis.org

464, 496, 696, 944, 4446, 4496, 4664, 6444, 6669, 6996, 9666, 9944, 44649, 44664, 44694, 44696, 44946, 44964, 46664, 46696, 49446, 49496, 49944, 64664, 66664, 66996, 69464, 69944, 69996, 94996, 96464, 96664, 96996, 99664, 99946, 99996

Offset: 1

Jonathan Vos Post, Nov 17 2005

			a(1) = 464 = 2^4 x 29, a(2) = 496 = 2^4 * 31, a(3) = 696 = 2^3 * 3 * 29, a(4) = 944 = 2^4 * 59, a(5) = 4446 = 2 * 3^2 * 13 * 19, a(6) = 4496 = 2^4 * 281, a(7) = 4664 = 2^3 * 11 * 53, a(8) = 6444 = 2^2 * 3^2 * 179, a(9) = 6669 = 3^3 * 13 * 19, a(10) = 6996 = 2^2 * 3 * 11 * 53.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358, A014614, A107665, A107666, A107342, A111494, A111496.

Table[Select[FromDigits/@Tuples[{4,6,9},n],PrimeOmega[#]==5&],{n,3,5}]//Flatten (* Harvey P. Dale, Dec 16 2024 *)

do(N)=my(v=List(), a=[4, 6, 9]); for(d=1, N, forvec(u=vector(d, i, [1, 3]), t=fromdigits(apply(n->a[n], u)); if(bigomega(t)==5, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Corrected by Ray Chandler, Nov 19 2005

A108614 Semiprimes with non-semiprimes digits (no digits 4,6,9 in semiprimes).

Original entry on oeis.org

10, 15, 21, 22, 25, 33, 35, 38, 51, 55, 57, 58, 77, 82, 85, 87, 111, 115, 118, 121, 122, 123, 133, 155, 158, 177, 178, 183, 185, 187, 201, 202, 203, 205, 213, 215, 217, 218, 221, 235, 237, 253, 278, 287, 301, 302, 303, 305, 321, 323, 327, 335, 355, 358, 371

Offset: 1

Zak Seidov, Jun 13 2005

Complement of A107342 in the class of semiprimes.

This is to semiprimes A001358 as A034844 (Primes with nonprime digits) is to primes A000040. [Jonathan Vos Post, Jul 15 2010]

Cf. A107342, A137167.

Cf. A107665, A107666, A111494, A111496, A111697, A179336. [Jonathan Vos Post, Jul 15 2010]

cnd[n_]:=Plus@@Last/@FactorInteger[n]==2&&Union[FreeQ[IntegerDigits[n], # ]&/@{4, 6, 9}]=={True};Select[Range[600], cnd[ # ]&]

{j in A001358 and j not in A179463}. [Jonathan Vos Post, Jul 15 2010]

A137167 Semiprimes that do not contain any other semiprimes as a substring.

Original entry on oeis.org

4, 6, 9, 10, 15, 21, 22, 25, 33, 35, 38, 51, 55, 57, 58, 77, 82, 85, 87, 111, 118, 123, 178, 183, 201, 202, 203, 205, 237, 278, 301, 302, 303, 305, 323, 327, 371, 501, 502, 505, 527, 537, 703, 707, 713, 717, 718, 723, 731, 737, 753, 781, 802, 803, 807, 813, 817

Offset: 1

Jonathan Vos Post, Apr 03 2008

Semiprime analog of A033274. If there is more than one digit, all digits must be nonsemiprime numbers {0,1,2,3,5,7,8}.

			Start with all semiprimes and sieve out the ones which have semiprime substrings. Semiprime A001358(5) = 14 is not in this sequence because it contains the digit "4" which is semiprime A001358(1). Semiprime A001358(35) = 106 is not in this sequence because it contains the digit "6" which is semiprime A001358(2) and also contains as substring "10" which is semiprime A001358(4).

Cf. A001358, A033274, A107342.

isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false ; fi ; end: Lton := proc(L) local a,i; a :=0 ; for i from 1 to nops(L) do a := 10*a+op(i,L) ; od: a ; end: isA137167 := proc(n) local dgs,strti,endi ; if isA001358(n) then dgs := ListTools[Reverse](convert(n,base,10)) ; for strti from 1 to nops(dgs) do for endi from strti to nops(dgs) do if strti > 1 or endi < nops(dgs) then if isA001358(Lton([op(strti..endi,dgs)])) then RETURN(false) : fi ; fi ; od: od: RETURN(true) ; else RETURN(false) ; fi ; end: for n from 1 to 1600 do if isA137167(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, Apr 12 2008

smQ[n_]:=PrimeOmega[n]==2&&NoneTrue[Select[Union[FromDigits/@ Flatten[ Table[Partition[IntegerDigits[n],i,1],{i,IntegerLength[n]-1}],1]], #>0&],PrimeOmega[#]==2&]; Select[Range[1000],smQ] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 26 2014 *)

More terms from R. J. Mathar, Apr 12 2008

A178755 Integers that become semiprime when any single digit is removed.

Original entry on oeis.org

44, 46, 49, 64, 66, 69, 94, 96, 99, 104, 155, 215, 221, 222, 225, 226, 251, 255, 262, 265, 333, 334, 335, 338, 339, 349, 355, 358, 385, 393, 394, 395, 469, 515, 551, 555, 557, 558, 577, 585, 587, 622, 625, 655, 695, 774, 777, 822, 825, 826, 855, 857, 862, 865

Offset: 1

Jonathan Vos Post, Jun 09 2010

The subsequence of semiprimes begins: 46, 49, 69, 94, 155, 215, 221, 226, 262, 265, 334, 335, 339, 355, 358, 393, 394, 395, 469, 515, 551, 622, 655, 695, 862, 865, 914, 933, 934, 951, 955, 1111, 1115, 1119, 1159, 1219, 1411, 1415, 1466, 2021, 2026, 2062, 2095, 2159, 2899, 2959, 2995, 2998, 3035, 3039, ....
The subsequence of primes begins: 251, 349, 557, 577, 587, 857, 877, 1559, 1669, 4111, 4973, 5051, 5119, 5519, 5591, 6299, 6679, 6871, 6899, 6949, 7213, 7789, 7949, 7993, 8669, 8699, 9133, 9221, 9551, 9749, ....
This is to semiprimes A001358 as A034895 is to primes A000040. Note that this is not a subset of A107342, as there are values with nonsemiprime digits, beginning with 104, 155, 215, 221, 222, ....

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

Cf. A001358, A034895, A107342.

 Select[Range[3000],Union[PrimeOmega[FromDigits/@Subsets[IntegerDigits[#],{IntegerLength[#]-1}]]]=={2}&] (* Harvey P. Dale, Apr 25 2015 *)

a(10) = 104 because deleting the "1" gives "04" which by OEIS protocol becomes the semiprime 4=2*2; deleting the "0" gives the semiprime 14=2*7; and deleting the "4" gives the semiprime 10=2*5.

Extended by Ray Chandler

A179463 Semiprimes A001358 containing at least one semiprime digit in base 10.

Original entry on oeis.org

4, 6, 9, 14, 26, 34, 39, 46, 49, 62, 65, 69, 74, 86, 91, 93, 94, 95, 106, 119, 129, 134, 141, 142, 143, 145, 146, 159, 161, 166, 169, 194, 206, 209, 214, 219, 226, 247, 249, 254, 259, 262, 265, 267, 274, 289, 291, 295, 298, 299, 309, 314, 319, 326, 329, 334, 339, 341

Offset: 1

Jonathan Vos Post, Jul 15 2010

Semiprimes containing at least one 4, 6, or 9 digit base 10.
This is to semiprimes A001358 as A179336 is to primes A000040.
This properly includes the subset A107342 Semiprimes with semiprime digits.

Cf. A107342 Semiprimes with semiprime digits (digits 4, 6, 9 only), A107665 Numbers with semiprime digits (digits 4, 6, 9 only), A107666 Primes with semiprime digits (digits 4, 6, 9 only), A111494, A111496, A111697, A108614 Semiprimes with non-semiprimes digits (no digits 4, 6, 9 in semiprimes), A179336.

spdQ[n_]:=Module[{idn=IntegerDigits[n]},MemberQ[idn,4] || MemberQ[ idn,6] || MemberQ[ idn,9]]; Select[Select[Range[350],PrimeOmega[#]==2&],spdQ] (* Harvey P. Dale, Jun 24 2013 *)

Corrected (a(37) added) by Harvey P. Dale, Jun 24 2013

A254715 Number of n-digit semiprimes with semiprime digits (4, 6, 9).

Original entry on oeis.org

3, 4, 8, 18, 55, 137, 415, 941, 2854, 7743, 21959, 61545, 175817, 496688

Offset: 1

Zak Seidov, Feb 06 2015

			a(1) = 3 because there are 3 one-digit semiprimes with semiprime digits: 4,6,9.
a(2) = 4 because there are 4 two-digit relevant semiprimes: 46,49,69,94.
a(3) = 8 because there are 8 three-digit relevant semiprimes: 446,466,469,649,669,694,699,949.

Cf. A107342.

a(n) = number of n-digit terms in A107342.

cp's OEIS Frontend

A107666 Primes having only {4, 6, 9} as digits.

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A107665 Numbers with semiprime digits (digits 4, 6, 9 only).

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A111494 3-almost primes with semiprime digits (digits 4, 6, 9 only).

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A111496 4-almost primes with semiprime digits (digits 4, 6, 9 only).

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A111697 5-almost primes with semiprime digits (digits 4, 6, 9 only).

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A108614 Semiprimes with non-semiprimes digits (no digits 4,6,9 in semiprimes).

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A137167 Semiprimes that do not contain any other semiprimes as a substring.

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A178755 Integers that become semiprime when any single digit is removed.

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