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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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A338049 a(n) is the smallest prime that is not less than prime(n) and is such that prime(n)*a(n)+2 is semiprime.

Original entry on oeis.org

2, 11, 11, 7, 11, 19, 17, 29, 29, 29, 37, 37, 43, 43, 61, 53, 61, 71, 89, 79, 73, 79, 83, 103, 97, 103, 107, 109, 113, 127, 131, 151, 137, 151, 157, 197, 167, 167, 173, 181, 211, 199, 191, 197, 199, 211, 227, 257, 257, 241, 233, 251, 257, 251, 263, 263, 269
Offset: 1

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Author

N. J. A. Sloane, Oct 08 2020, based on an email from Todor Szimeonov, Oct 07 2020

Keywords

Comments

Motivated by a question about arranging square tiles in a rectangle.

Crossrefs

Cf. A000040, A001358, A092207, A198327, A338048.

A180245 n-th natural number m such that m and m+2 are both divisible by exactly n primes (counted with multiplicity).

Original entry on oeis.org

3, 33, 42, 196, 918, 6640, 24750, 246078, 781248, 6565374, 25227774, 165009150, 673932798, 5268548608, 25737162750, 179511912448, 818179991550, 4228689854464, 26455088693248, 104384041582590, 820632501420030
Offset: 1

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Author

Jonathan Vos Post, Aug 19 2010

Keywords

Comments

Main diagonal A[n,n] of A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity).
This is the main diagonal of the array mentioned in A180117, A180150, and A180151.
Row 1 = A001359 = the lesser of twin primes.
Row 2 = A092207 = Numbers n such that n and n+2 are semiprimes.
Row 3 = A180117 = m and m+2 are both divisible by exactly 3 primes (counted with multiplicity).
Row 4 = A180150 = m and m+2 are both divisible by exactly 4 primes (counted with multiplicity).
Row 5 = A180151 = m and m+2 are both divisible by exactly 5 primes (counted with multiplicity).

Examples

			a(1) = 3 because 3 is the first natural number m such that m and m+2 are both divisible by exactly 1 prime (i.e., the first of the lesser of twin primes).
a(2) = 33 because that is the 2nd natural number m such that m and m+2 are both divisible by exactly 2 primes (i.e. 33 = 3 * 11 is semiprime and when 2 is added becomes 35 = 5 * 7 which is also semiprimes) the 1st such being 4.

Crossrefs

Cf. A001359, A092207, A180117, A180150, A180151.

Extensions

Corrected and extended by Jack Brennen, D. S. McNeil and Ray Chandler, Aug 19 2010
a(16)-a(21) from Donovan Johnson, Aug 27 2010
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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