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.

Previous Showing 31-33 of 33 results.

A176888 Unsafe primes minus 1.

Original entry on oeis.org

1, 2, 12, 16, 18, 28, 30, 36, 40, 42, 52, 60, 66, 70, 72, 78, 88, 96, 100, 102, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 172, 180, 190, 192, 196, 198, 210, 222, 228, 232, 238, 240, 250, 256, 268, 270, 276, 280, 282, 292, 306, 310, 312, 316, 330, 336
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 28 2010

Keywords

Comments

Non-semiprimes k such that k+1 is a prime.

Crossrefs

Intersection of A006093 and A100959.

Programs

Formula

a(n) = A059456(n) - 1.
a(n) ~ n log n. - Charles R Greathouse IV, Dec 29 2024

Extensions

Entries checked by R. J. Mathar, May 06 2010

A178928 Smallest semiprime containing leading sequence of n ascending numbers.

Original entry on oeis.org

10, 121, 123, 1234, 123451, 1234561, 1234567, 123456782, 12345678911, 123456789101, 123456789101117, 12345678910111229, 123456789101112133, 123456789101112131414, 1234567891011121314159
Offset: 1

Views

Author

Jonathan Vos Post, Dec 30 2010

Keywords

Comments

This is to semiprimes A001358 as A053546 is to primes A000040.

Examples

			a(1) = 10 because 10 = 2 * 5 is the smallest semiprime (or biprime, products of two primes) whose leftmost (base 10) digit is 1.
a(2) = 121 because 121 = 11^2 semiprime whose leftmost digits are 12.
a(3) = 123 since it is a semiprime already.
a(4) = 1234 = 2 * 617.
a(5) = 123451 = 41 * 3011.
a(6) = 1234561 = 211 * 5851.

Crossrefs

Cf. A001358, A053546, A100959.

Programs

  • Mathematica
    semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 0, m = FromDigits@ Flatten@ IntegerDigits@ Range@ n}, If[ semiPrimeQ@ m, , While[a = 10^(1 + Max[0, Floor@ Log10@ k]) m + k; ! semiPrimeQ@ a, k++]; m = a]; m]; Array[f, 15]

A209292 Non-semiprimes n such that 2n+1 are non-semiprimes.

Original entry on oeis.org

1, 2, 3, 5, 8, 11, 13, 18, 20, 23, 29, 30, 31, 36, 37, 40, 41, 44, 48, 50, 52, 53, 54, 56, 63, 67, 68, 73, 75, 76, 78, 81, 83, 89, 90, 96, 97, 98, 99, 103, 105, 112, 113, 114, 116, 120, 125, 127, 128, 130, 131, 135, 136, 137, 138, 139, 140, 148, 153, 156
Offset: 1

Views

Author

Jonathan Vos Post, Jan 16 2013

Keywords

Comments

This is to A005384 as nonsemiprimes A100959 are to primes A000040.

Examples

			a(1) = 1 because 1 is not a semiprime (the smallest semiprime is 4), and 2*1 + 1 = 3 is not a semiprime.
7 is not a semiprime, but 2*7 + 1 = 15 = 3*5 is a semiprime, so 7 is not in this sequence.

Crossrefs

Cf. A001358, A005384, A100959, A209271.

Programs

  • Mathematica
    SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; Select[Range[200], ! SemiPrimeQ[#] && ! SemiPrimeQ[2 # + 1] &] (* T. D. Noe, Jan 17 2013 *)
  • PARI
    is(n)=bigomega(n)!=2 && bigomega(2*n+1)!=2 \\ Charles R Greathouse IV, Jan 16 2013

Formula

{n such that n is in A100959, and 2*n + 1 is in A100959} = {n such that n is not in A001358, and 2*n + 1 is not in A001358}.
a(n) ~ n. - Charles R Greathouse IV, Jan 16 2013
Previous Showing 31-33 of 33 results.

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

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