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.

Showing 1-3 of 3 results.

A108631 Semiprimes with nonprime digits (no digits 2,3,5,7 in semiprimes).

Original entry on oeis.org

4, 6, 9, 10, 14, 46, 49, 69, 86, 91, 94, 106, 111, 118, 119, 141, 146, 161, 166, 169, 194, 411, 446, 466, 469, 481, 489, 611, 614, 649, 669, 681, 689, 694, 698, 699, 818, 841, 849, 866, 869, 886, 889, 898, 899, 901, 914, 949, 961, 989, 998
Offset: 1

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Comments

Complement of 108632 in the class of semiprimes.

Crossrefs

Cf. A108632.

Programs

  • Mathematica
    Select[Range[1000],PrimeOmega[#]==2&&ContainsOnly[IntegerDigits[#],{0,1,4,6,8,9}]&] (* Harvey P. Dale, Aug 15 2017 *)

A178423 Semiprimes for which dropping any digit gives a prime number.

Original entry on oeis.org

22, 25, 33, 35, 55, 57, 77, 111, 119, 371, 411, 413, 417, 437, 471, 473, 611, 671, 713, 731, 1037, 1073, 1079, 1379, 1397, 1673, 1739, 1937, 1991, 2571, 2577, 2811, 3113, 3131, 3173, 3317, 4331, 4439, 4499, 4631, 6017, 6431, 6773, 7619, 9977, 12777
Offset: 1

Views

Author

Jonathan Vos Post, May 27 2010

Keywords

Comments

This is the 2nd row of the infinite array A[k,n] = n-th number with k prime factors (not necessarily distinct) for which dropping any digit gives a prime number.
The first row A[1,n] = A051362 = numbers n such that n remains prime if any digit is deleted (zeros allowed).
The 3rd row A[3,n] begins {27 = 3^3, 52 = 2^2 * 13, 75 = 3 * 5^2, 117 = 3^2 * 13, 171 = 3^2 * 19, ...}.
The 4th row A[4,n] begins: {2277 = 3^2 * 11 * 23, 5577 = 3 * 11 * 13^2, 8211 = 3 * 7 * 17 * 23, 8811 = 3^2 * 11 * 89, ...}.
The 5th row A[5,n] begins:{32 = 2^5, 72 = 2^3 x 3^2, ...}.

Examples

			a(9) = 119 because this is a semiprime (119 = 7 * 17), dropping the leftmost digit gives 19 (a prime), dropping the middle digit gives 19 (a prime), and dropping the rightmost digit gives 11 (a prime).

Links

Crossrefs

Cf. A000040, A001358, A034895, A108632.

Programs

  • Mathematica
    ddp[n_]:=Module[{idn=IntegerDigits[n]},PrimeOmega[n]==2 && And@@PrimeQ[ FromDigits/@Table[Drop[idn,{i}],{i,Length[idn]}]]]; Select[Range[ 13000],ddp] (* Harvey P. Dale, Apr 10 2012 *)

Formula

A001358 INTERSECTION A034895.

A242739 Semiprimes having only straight digits.

Original entry on oeis.org

4, 14, 74, 77, 111, 141, 177, 411, 417, 447, 471, 717, 771, 1111, 1114, 1141, 1147, 1174, 1177, 1411, 1417, 1441, 1477, 1711, 1714, 1717, 1774, 4117, 4141, 4171, 4174, 4411, 4414, 4417, 4471, 4474, 4711, 4714, 4717, 4741, 4747, 4771, 4777, 7111, 7114, 7117, 7141
Offset: 1

Views

Author

K. D. Bajpai, May 21 2014

Keywords

Comments

A straight digit semiprime has only the straight digits, i.e., 1, 4 or 7.
Intersection of A001358 and A028373. - Michel Marcus, May 25 2014

Examples

			471 = 3 * 157 is semiprime and has only straight digits 4, 7 and 1. Hence it is in the sequence.
1147 =  31 * 37 is semiprime and has only straight digits 1, 1, 4 and 7. Hence it is in the sequence.

Links

Crossrefs

Cf. A001358, A028373, A079651, A108631, A108632.

Programs

  • Mathematica
    A242739 = {}; Do[a = PrimeOmega[n]; If [a == 2 && Intersection[IntegerDigits[n], {0, 2, 3, 5, 6, 8, 9}] == {}, AppendTo[A242739, n]], {n, 8000}]; A242739
Table[Select[FromDigits/@Tuples[{1,4,7},n],PrimeOmega[#]==2&],{n,4}]//Flatten (* Harvey P. Dale, Sep 23 2022 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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