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.

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A115687 Powerful(1) numbers (A001694) whose digit reversal is a semiprime (A001358).

Original entry on oeis.org

4, 9, 49, 64, 121, 169, 289, 400, 512, 625, 900, 961, 968, 1156, 1225, 1568, 1849, 2048, 2401, 2888, 3125, 3136, 3364, 3481, 3721, 4000, 4900, 4913, 5041, 5329, 5408, 6400, 6859, 6889, 7396, 8192, 8575, 9000, 9604, 10201, 10648, 10816, 10952
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			968=2^3*11^2 is powerful and 869=11*79 is semiprime.

Links

Crossrefs

Cf. A001358, A001694, A115688.

A115688 Semiprimes (A001358) whose digit reversal is a powerful(1) number (A001694).

Original entry on oeis.org

4, 9, 10, 46, 94, 121, 169, 215, 526, 869, 961, 982, 1042, 1273, 1405, 1843, 2918, 3194, 4069, 4633, 5213, 5221, 5758, 6313, 6511, 6937, 8045, 8402, 8651, 8882, 9235, 9481, 9586, 9886, 10201, 10609, 12538, 12769, 14023, 16171, 16327, 16582
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			869=11*79 is semiprime and 968=2^3*11^2 is powerful.

Links

Crossrefs

Cf. A001358, A001694, A115687.

Programs

  • Maple
    N:= 99999:
S:= {1}:
p:= 1:
do
  p:= nextprime(p);
  if p^2 > N then break fi;
  S:= S union map(t -> seq(t*p^j,j=2..floor(log[p](N/t))), S);
od:
digrev:= proc(x) local L;
  L:= convert(x,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
sort(convert({10} union select(t -> numtheory:-bigomega(t)=2, map(digrev, select(t -> t mod 10 <> 0, S))),list)); # Robert Israel, Dec 03 2019

A115708 Semiprimes (A001358) whose digit reversal is a pentagonal number (A000326).

Original entry on oeis.org

10, 15, 21, 22, 235, 287, 517, 529, 671, 1513, 1555, 2611, 5137, 5331, 6241, 7017, 7171, 7421, 7597, 7814, 10078, 10913, 15011, 15094, 15214, 15251, 20395, 20603, 21542, 23129, 24501, 24873, 25157, 26851, 27161, 51998, 53297, 54989, 55551
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			235=5*47 is semiprime and 532 is the 19th pentagonal number.

Links

Crossrefs

Cf. A000326, A001358, A115709.

Programs

  • Mathematica
    Select[Range[60000],PrimeOmega[#]==2&&IntegerQ[(1+Sqrt[1+24* IntegerReverse[#]])/ 6]&] (* Harvey P. Dale, Apr 27 2022 *)

A115710 Semiprimes (A001358) whose digit reversal is a square.

Original entry on oeis.org

4, 9, 10, 46, 94, 121, 169, 526, 961, 982, 1042, 1273, 1405, 1843, 4069, 4633, 5221, 6313, 6511, 6937, 9235, 9481, 9886, 10201, 10609, 12538, 12769, 14023, 16171, 16327, 16582, 16723, 18085, 18463, 18811, 40219, 42817, 42931, 44353, 44521
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			46=2*23 is semiprime and 64=8^2.

Crossrefs

Cf. A001358, A115711.

Programs

  • Mathematica
    Select[Range[50000],PrimeOmega[#]==2&&IntegerQ[Sqrt[FromDigits[ Reverse[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Mar 03 2013 *)

A115711 Squares whose digit reversal is a semiprime (A001358).

Original entry on oeis.org

4, 9, 49, 64, 121, 169, 289, 400, 625, 900, 961, 1156, 1225, 1849, 2401, 3136, 3364, 3481, 3721, 4900, 5041, 5329, 6400, 6889, 7396, 9604, 10201, 10816, 11449, 11881, 12100, 12544, 12769, 13225, 13456, 13924, 15376, 15625, 16129, 16384, 16900
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			64=8^2 and 46=2*23 is semiprime.

Crossrefs

Cf. A001358, A115710.

Programs

  • Mathematica
    Select[Range[150]^2,PrimeOmega[FromDigits[Reverse[ IntegerDigits[ #]]]]==2&] (* Harvey P. Dale, Sep 20 2011 *)

A115742 Triangular numbers whose digit reversal is a semiprime (A001358).

Original entry on oeis.org

6, 15, 28, 55, 78, 105, 120, 190, 496, 780, 903, 946, 1176, 1225, 1275, 1540, 1653, 1770, 1830, 1891, 2080, 3081, 3403, 3486, 3570, 3741, 3916, 4186, 4753, 5050, 5356, 5671, 6670, 7021, 7140, 7381, 7503, 7626, 8515, 8911, 9316, 9591, 9870
Offset: 1

Views

Author

Giovanni Resta, Jan 31 2006

Keywords

Examples

			15=T(5) and 51=3*17 is semiprime.

Links

Crossrefs

Cf. A001358, A115741.

Programs

  • Mathematica
    Select[Accumulate[Range[200]],PrimeOmega[FromDigits[Reverse[ IntegerDigits[ #]]]] == 2&] (* Harvey P. Dale, Nov 14 2013 *)

A116001 sigma(n) - phi(n) gives a semiprime (A001358).

Original entry on oeis.org

6, 10, 18, 20, 22, 27, 34, 40, 49, 52, 58, 64, 68, 82, 98, 100, 118, 136, 142, 144, 148, 160, 162, 164, 202, 212, 214, 242, 243, 244, 274, 288, 289, 298, 320, 325, 333, 338, 343, 356, 358, 361, 382, 392, 394, 404, 436, 441, 454, 464, 478, 512, 538, 544, 548
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			sigma(100)-phi(100)=177=3*59

Links

Crossrefs

Cf. A001358, A116017, A116000.

Programs

  • Mathematica
    Select[Range[600],PrimeOmega[DivisorSigma[1,#]-EulerPhi[#]]==2&] (* Harvey P. Dale, Mar 18 2013 *)

A116024 The n-th prime minus n gives a semiprime (A001358).

Original entry on oeis.org

5, 7, 9, 12, 20, 22, 24, 36, 40, 49, 52, 55, 58, 59, 60, 64, 69, 72, 74, 78, 80, 82, 87, 93, 96, 101, 105, 106, 108, 112, 114, 117, 118, 122, 123, 124, 125, 128, 132, 134, 135, 136, 138, 140, 142, 147, 150, 156, 158, 159, 160, 162, 164, 166, 170, 172, 180, 184
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			p(40)-40=133=7*19.

Links

Crossrefs

Cf. A001358, A116013, A116023.

Programs

  • Mathematica
    Transpose[Select[Table[{Prime[n],n},{n,200}],PrimeOmega[#[[1]]-#[[2]]] == 2&]][[2]] (* Harvey P. Dale, Jun 05 2015 *)

A116039 Numbers k such that k + prime(k) + prime(prime(k)) is a semiprime (A001358).

Original entry on oeis.org

1, 2, 8, 9, 11, 12, 18, 19, 22, 23, 26, 29, 33, 35, 43, 47, 50, 53, 57, 59, 61, 69, 75, 76, 77, 78, 81, 89, 103, 105, 109, 112, 124, 125, 131, 135, 140, 141, 142, 143, 146, 151, 153, 155, 160, 166, 170, 175, 176, 177, 181, 189, 209, 211, 215, 216, 220, 225, 226
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			112 is in the sequence since 112 + prime(112) + prime(prime(112)) = 5242 = 2*2621.

Links

Crossrefs

Cf. A001358, A116038.

Programs

  • Maple
    with(numtheory): A116039:=n->`if`(bigomega(n+ithprime(n)+ithprime(ithprime(n))) = 2, n, NULL): seq(A116039(n), n=1..500); # Wesley Ivan Hurt, Jun 23 2015

A116935 Semiprimes (A001358) which are the concatenation of the numbers 1 through n for some n.

Original entry on oeis.org

123, 1234, 1234567, 12345678910111213141516171819202122232425262728293031323334
Offset: 1

Views

Author

Jonathan Vos Post, Mar 20 2006

Keywords

Comments

Next term has 185 digits, and it is thus too large to be included. It is equal to the concatenation of the first 97 integers. - Giovanni Resta, Jun 15 2016

Examples

			a(1) = 123 = 3 * 41.
a(2) = 1234 = 2 * 617.
a(3) = 1234567 = 127 * 9721.
a(4) = 2 * 6172839455055606570758085909601061116212631364146515661667.

Crossrefs

Cf. A001358, A007908.

Formula

{A007908} intersect {A001358}.
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