A110605 -id:A110605 - cp's OEIS frontend

A110603 Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.

4, 5, 9, 11, 12, 18, 19, 31, 36, 37, 38, 43, 44, 46, 47, 48, 51, 52, 53, 58, 59, 61, 76, 77, 78, 84, 86, 88, 94, 96, 103, 106, 108, 112, 128, 131, 146, 147, 148, 151, 156, 159, 161, 168, 171, 172, 177, 178, 181, 184, 194, 196, 198, 208, 212, 218, 223, 226, 227, 228

Offset: 1

Jonathan Vos Post, Jul 30 2005

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 5) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 5 because 5 (base 5) = 10 and 10 (base 10) = 2 * 5.
a(3) = 9 because 9 (base 5) = 14 and 14 (base 10) = 2 * 7.
a(4) = 11 because 11 (base 5) = 21 and 21 (base 10) = 3 * 7.
a(5) = 12 because 12 (base 5) = 22 and 22 (base 10) = 2 * 11.

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

Cf. A001358, A007091, A108873, A110602, A110604, A110605, A110606, A110607.

Select[Range[228], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 5]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)
Select[Range[300],PrimeOmega[FromDigits[IntegerDigits[#,5],10]]==2&] (* Harvey P. Dale, Aug 14 2023 *)

Corrected and extended by Ray Chandler, Aug 05 2005

A110607 Numbers n whose base 9 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 6, 9, 13, 14, 19, 20, 23, 24, 30, 31, 32, 35, 42, 46, 50, 52, 53, 56, 59, 67, 70, 74, 77, 78, 79, 87, 91, 95, 98, 100, 101, 102, 111, 112, 118, 119, 120, 122, 123, 131, 134, 136, 141, 151, 152, 156, 158, 160, 163, 164, 165, 167, 168, 174, 175, 176, 178, 179, 181

Offset: 1

Jonathan Vos Post, Jul 30 2005

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8.

			a(1) = 4 because 4 (base 9) = 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 9) = 6 (base 10) = 2 * 3.
a(3) = 9 because 9 (base 9) = 10 and 10 (base 10) = 2 * 5.
a(4) = 13 because 13 (base 9) = 14 and 14 (base 10) = 2 * 7.
a(5) = 14 because 14 (base 9) = 15 and 15 (base 10) = 3 * 5.

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

Cf. A001358, A007095, A108873, A110602, A110603, A110604, A110605, A110607.

Select[Range[181], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 9]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)
Select[Range[200],PrimeOmega[FromDigits[IntegerDigits[#,9]]]==2&] (* Harvey P. Dale, Dec 02 2018 *)

Extended by Ray Chandler, Aug 05 2005

A108873 Numbers n whose base 3 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

3, 7, 8, 13, 16, 17, 19, 20, 25, 31, 37, 40, 43, 47, 49, 61, 64, 65, 71, 73, 82, 88, 89, 92, 97, 100, 101, 106, 110, 115, 118, 121, 127, 136, 142, 143, 155, 179, 184, 187, 188, 191, 209, 232, 235, 244, 250, 254, 259, 262, 263, 265, 269, 274, 281, 289, 299, 314, 319

Offset: 1

Jonathan Vos Post, Jul 13 2005

			a(1) = 3 because 3 (base 10) = 10 (base 3) and 10 base 10 = 2 * 5.
a(2) = 7 because 7 (base 10) = 21 (base 3) and 21 base 10 = 3 * 7.
a(4) = 13 because 13 (base 10) = 111 (base 3) and 111 base 10 = 3 * 37.
a(12) = 40 because 40 (base 10) = 1111 (base 3) and 1111 base 10 = 11 * 101.
a(21) = 82 because 82 (base 10) = 10001 (base 3) and 10001 base 10 = 73 * 137.
a(26) = 100 because 100 (base 10) = 10201 (base 3) and 10201 base 10 = 101^2.

Cf. A001358, A007089.

Cf. A110602 (base 4), A110603 (base 5), A110604 (base 6), A110605 (base 7) , A110606 (base 8), A110607 (base 9).

with(numtheory): a:=proc(n) local nn, nnn: nn:=convert(n,base,3): nnn:=add(nn[j]*10^(j-1),j=1..nops(nn)): if bigomega(nnn)=2 then n else fi end: seq(a(n),n=1..350); # Emeric Deutsch, Jul 16 2005

Select[Range[319], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 3]]] == 2 &] (* Ray Chandler, Sep 21 2005*)

More terms from Emeric Deutsch, Jul 16 2005

A110602 Numbers n whose base 4 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 9, 10, 15, 21, 25, 26, 27, 31, 33, 34, 35, 39, 41, 49, 50, 51, 57, 59, 67, 69, 81, 85, 89, 95, 98, 99, 101, 119, 122, 127, 137, 141, 143, 145, 146, 147, 154, 155, 161, 173, 178, 185, 187, 199, 202, 205, 209, 211, 215, 221, 223, 226, 235, 239, 257, 259, 265, 266

Offset: 1

Jonathan Vos Post, Jul 30 2005

Note that this sequence begins with 7 semiprimes (A001358) but is not a subset of the semiprimes, since a(9) = 31 and 31 (base 4) = 133, which interpreted as base 10 is 133 = 7 * 19, yet 31 (base 10) is prime rather than semiprime. A108873 is the equivalent using base 3. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 4) = 10 and 10 (base 10) = 2 * 5, a semiprime (A001358).
a(2) = 9 because 10 (base 4) = 21, which interpreted base 10 is 21 = 3 * 7.
a(3) = 10 because 10 (base 4) = 22, which interpreted base 10 is 22 = 2 * 11.
a(4) = 15 because 15 (base 4) = 33, which interpreted base 10 is 33 = 3 * 11.

Cf. A001358, A007090, A108873, A110603, A110604, A110605, A110606, A110607.

Select[Range[266], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 4]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Extended by Ray Chandler, Aug 05 2005

A110604 Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 6, 10, 11, 13, 14, 17, 21, 22, 23, 31, 35, 43, 47, 49, 50, 51, 57, 58, 61, 62, 63, 65, 71, 73, 74, 75, 77, 81, 82, 83, 85, 95, 105, 106, 109, 110, 111, 113, 118, 121, 123, 130, 131, 133, 143, 147, 151, 153, 155, 158, 173, 175, 177, 178, 181, 182, 185, 187, 190, 191

Offset: 1

Jonathan Vos Post, Jul 30 2005

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 6) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 6) = 10 and 10 (base 10) = 2 * 5.
a(3) = 10 because 10 (base 6) = 14 and 14 (base 10) = 2 * 7.
a(4) = 11 because 11 (base 6) = 15 and 15 (base 10) = 3 * 5.
a(5) = 13 because 13 (base 6) = 21 and 21 (base 10) = 3 * 7.

Cf. A001358, A007092, A108873, A110602, A110603, A110605, A110606, A110607.

Select[Range[191], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 6]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)
Select[Range[200],PrimeOmega[FromDigits[IntegerDigits[#,6]]]==2&] (* Harvey P. Dale, Oct 02 2011 *)

Corrected and extended by Ray Chandler, Aug 05 2005

A110606 Numbers n whose base 8 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 6, 8, 12, 13, 17, 18, 21, 22, 27, 28, 29, 38, 41, 45, 47, 50, 53, 60, 63, 70, 73, 77, 81, 82, 83, 91, 92, 97, 98, 99, 101, 102, 109, 113, 118, 127, 129, 130, 131, 133, 134, 139, 140, 141, 143, 145, 150, 157, 159, 167, 171, 172, 178, 181, 183, 188, 193, 194, 195

Offset: 1

Jonathan Vos Post, Jul 30 2005

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 8) = 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 8) = 6 (base 10) = 2 * 3.
a(3) = 8 because 8 (base 8) = 10 and 10 (base 10) = 2 * 5.
a(4) = 12 because 12 (base 8) = 14 and 14 (base 10) = 2 * 7.
a(5) = 13 because 13 (base 8) = 15 and 15 (base 10) = 3 * 5.

Cf. A001358, A007094, A108873, A110602, A110603, A110604, A110605, A110607.

Select[Range[195], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 8]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Extended by Ray Chandler, Aug 05 2005

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A110603 Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.

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A110607 Numbers n whose base 9 representations, interpreted as base 10 integers, are semiprimes.

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A108873 Numbers n whose base 3 representations, interpreted as base 10 integers, are semiprimes.

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A110602 Numbers n whose base 4 representations, interpreted as base 10 integers, are semiprimes.

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A110604 Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.

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A110606 Numbers n whose base 8 representations, interpreted as base 10 integers, are semiprimes.

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