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 1-6 of 6 results.

A100915 Numbers n such that n plus n-th semiprime is semiprime.

Original entry on oeis.org

4, 6, 9, 12, 16, 18, 19, 20, 24, 29, 31, 34, 35, 39, 40, 44, 46, 49, 51, 54, 55, 72, 73, 76, 79, 80, 81, 84, 87, 91, 93, 94, 96, 98, 110, 113, 116, 120, 128, 130, 136, 137, 148, 150, 154, 159, 165, 168, 170, 172, 175, 188, 190, 191, 199, 200, 206, 215, 217, 220, 230
Offset: 1

Views

Author

Ray Chandler, Nov 26 2004

Keywords

Comments

This is the semiprime analog of A064402.

Examples

			a(3) = 9 because 9 + semiprime(9) = 9 + 25 = 34 is semiprime.

Links

Crossrefs

Cf. A001358, A064402, A100493, A100466, A100467, A100916.

Programs

  • Mathematica
    With[{c=Select[Range[1000],PrimeOmega[#]==2&]},Transpose[Select[Thread[ {c,Range[ Length[c]]}], PrimeOmega[Total[#]]==2&]][[2]]] (* Harvey P. Dale, Oct 25 2011 *)

Formula

a(n) = A100466(n) - A100916(n) = A100466(n) - A001358(A100915(n)).

A100466 Semiprimes of special form: sum of an integer k and the k-th semiprime.

Original entry on oeis.org

14, 21, 34, 46, 62, 69, 74, 77, 93, 115, 122, 129, 141, 158, 161, 177, 187, 194, 206, 215, 221, 289, 291, 302, 326, 329, 334, 346, 361, 382, 391, 393, 398, 403, 451, 471, 481, 502, 535, 543, 581, 583, 629, 635, 655, 674, 698, 706, 713, 723, 734, 802, 813
Offset: 1

Views

Author

Jonathan Vos Post, Nov 20 2004

Keywords

Comments

This is the semiprime analog of A061068.

Examples

			a(3) = 34 because 34 is the third semiprime appearing in A100493.

Links

  • Eric Weisstein, World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A061068, A100493, A100467, A100915, A100916.

Formula

a(n) = A100915(n) + A100916(n) = A100915(n) + A001358(A100915(n)).

Extensions

Edited, corrected and extended by Ray Chandler, Nov 26 2004

A100467 Semiprimes of special form: sum of a semiprime k and the k-th semiprime.

Original entry on oeis.org

14, 21, 34, 129, 141, 158, 187, 194, 206, 221, 361, 382, 391, 393, 674, 893, 922, 934, 1067, 1094, 1133, 1293, 1415, 1441, 1473, 1569, 1589, 1681, 1703, 1739, 1769, 1982, 2119, 2206, 2362, 2395, 2433, 2481, 2507, 2602, 2614, 2627, 2642, 2823, 2839, 2983
Offset: 1

Views

Author

Jonathan Vos Post, Nov 20 2004

Keywords

Examples

			34 is in the sequence because both 9 and 9+semiprime(9) = 9+25 = 34 are semiprimes.

Links

  • Eric Weisstein, World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A100493, A100466, A100915, A100916.

Extensions

Edited, corrected and extended by Ray Chandler, Nov 26 2004

A100916 Sum of a semiprime and its semiprime index is a new semiprime.

Original entry on oeis.org

10, 15, 25, 34, 46, 51, 55, 57, 69, 86, 91, 95, 106, 119, 121, 133, 141, 145, 155, 161, 166, 217, 218, 226, 247, 249, 253, 262, 274, 291, 298, 299, 302, 305, 341, 358, 365, 382, 407, 413, 445, 446, 481, 485, 501, 515, 533, 538, 543, 551, 559, 614, 623, 626
Offset: 1

Views

Author

Ray Chandler, Nov 26 2004

Keywords

Comments

This is the semiprime analog of A061067.

Examples

			a(1) = 10 because 10 = semiprime(4) and semiprime(4) + 4 = 14 is
semiprime.
a(2) = 15 because 15 = semiprime(6) and semiprime(6) + 6 = 21 is
semiprime.

Links

  • Eric Weisstein, World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A061067, A100493, A100466, A100467, A100915.

Programs

  • Mathematica
    Module[{sp=Select[Range[1000],PrimeOmega[#]==2&],len},len=Length[sp];Select[ Thread[{sp,Range[len]}],PrimeOmega[Total[#]]==2&]][[All,1]] (* Harvey P. Dale, Jan 13 2019 *)

Formula

a(n) = A100466(n) - A100915(n) = A001358(A100915(n)).

A173477 Semiprimes having no representation of the form semiprime(n)-+n, where semiprime(n) = A001358(n).

Original entry on oeis.org

10, 15, 25, 26, 35, 38, 39, 58, 65, 82, 85, 87, 91, 94, 118, 119, 121, 123, 133, 134, 142, 143, 155, 166, 183, 185, 201, 202, 209, 213, 217, 226, 237, 253, 267, 274, 278, 287, 295, 298, 299, 301, 303, 305, 314, 319, 321, 339, 355, 362, 371, 377, 381, 395, 407, 413, 415, 417, 422, 427
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 22 2010

Keywords

Examples

			Listing the first eight terms of A001358 gives us:
n: 1, 2, 3,  4,  5,  6,  7,  8, ...
   4, 6, 9, 10, 14, 15, 21, 22, ...
We see that 4 can be represented as 6-2, 6 can be represented as 4+2 or 9-3 or 10-4, 9 can be represented as 14-5 or 15-6, but 10 cannot be represented by any such sum or difference as 4+1, 6+2, 9+3, 14-5, 15-6, 21-7, and also any difference A001358(n)-n after that will miss it. Thus 10 is the first semiprime included in this sequence.

Links

Crossrefs

Cf. A001358, A100493, A172096.

Programs

  • Maple
    N:= 2000: # to use semiprimes <= N
Primes:= select(isprime, [2,seq(i,i=3..N,2)]):
Semiprimes:= select(`<=`,{seq(seq(Primes[i]*Primes[j],i=1..j),j=1..nops(Primes))},N):
sort(convert(Semiprimes minus {seq}(i+Semiprimes[i],i=1..nops(Semiprimes)) minus {seq}(Semiprimes[i]-i,i=1..nops(Semiprimes))),list)); # Robert Israel, Dec 20 2015

Extensions

Corrected by D. S. McNeil, Nov 23 2010
Name clarified and Example section added by Antti Karttunen, Dec 20 2015

A173638 The n-th semiprime plus n gives a palindrome in base 10.

Original entry on oeis.org

1, 2, 11, 17, 20, 23, 25, 35, 40, 48, 53, 59, 69, 86, 94, 100, 128, 133, 138, 141, 145, 194, 211, 216, 224, 232, 282, 326, 450, 615, 665, 824, 876, 929, 1171, 1197, 1267, 1290, 1293, 1450, 1498, 1520, 1566, 1655, 1790, 1898, 2248, 2313, 2624, 2786, 2826, 2849, 2912, 3058, 3082, 3098, 3270, 3290, 3408, 3586, 3610, 3672, 3792, 3912, 3945, 3982, 4000
Offset: 1

Views

Author

Jonathan Vos Post, Nov 23 2010

Keywords

Comments

This is to semiprimes A001358 as A115884 is to primes A000040.

Examples

			a(1) = 1 because 1st semiprime = 4, 4+1=5 is trivially a palindrome.
a(2) = 2 because 2nd semiprime = 6, 6+2=8 is trivially a palindrome.
a(3) = 11 because 11th semiprime = 33, 33+11=44 is nontrivially a palindrome.
a(4) = 17 because 17th semiprime = 49, 49+17=66 is nontrivially a palindrome.
a(5) = 20 because 20th semiprime = 57, 57+20=77 is nontrivially a palindrome.
a(8) = 35 because 35th semiprime = 106, 106+35=141 is nontrivially a palindrome.

Links

Crossrefs

A001358, A002113, A115884, A100493.

Programs

  • Mathematica
    Module[{nn=20000,sems},sems=Select[Range[nn],PrimeOmega[#]==2&]; Select[ Thread[{Range[Length[sems]],sems}],Total[ #]==IntegerReverse[Total[ #]]&]] [[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 08 2016 *)

Formula

{n: n + A001358(n) is in A002113} == {n: n + A001358(n) = R(n)} == {n: n + A001358(n) = A004086(n)}.
Showing 1-6 of 6 results.

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