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.

A122467 Write n-th semiprime in binary, sum as if decimal numbers.

Original entry on oeis.org

100, 210, 1211, 2221, 3331, 4442, 14543, 24653, 35654, 46664, 146665, 246675, 346686, 446796, 546907, 648017, 758018, 868029, 978140, 1089141, 1200151, 1311261, 2311262, 3311363, 4312373, 5313474, 6323484, 7333585, 8343695
Offset: 1

Views

Author

Jonathan Vos Post, Sep 09 2006

Keywords

Comments

Partial sum of A122466. Write n-th semiprime in binary, sum as if decimal numbers. Primes in this sequence begin a(4) = 2221, a(5) = 3331, a(7) = 14543 and a(34) = 13398139.

Examples

			a(4) = 100 + 110 + 1001 + 1010 = 2221 because the first 4 semiprimes can be written in binary as 100_2 + 110_2 + 1001_2 + 1010_2.
a(34) = 100 + 110 + 1001 + 1010 + 1110 + 1111 + 10101 + 10110 + 11001 + 11010 + 100001 + 100010 + 100011 + 100110 + 100111 + 101110 + 110001 + 110011 + 110111 + 111001 + 111010 + 111110 + 1000001 + 1000101 + 1001010 + 1001101 + 1010010 + 1010101 + 1010110 + 1010111 + 1011011 + 1011101 + 1011110 + 1011111 = 13398139 is prime.

Crossrefs

Cf. A000040, A001358, A007088, A004676, A122466.

Formula

a(n) = SUM[i=1..n]A122466(i) = SUM[i=1..n]A007088(A001358(i)).

A178043 n-th semiprime minus number of distinct transpositions of digits (zeros and units) in n-th semiprime written in base 2.

Original entry on oeis.org

1, 3, 3, 4, 10, 14, 11, 12, 15, 16, 18, 19, 15, 18, 24, 31, 29, 36, 49, 42, 43, 56, 44, 34, 39, 42, 47, 50, 51, 66, 70, 72, 73, 88, 71, 104, 94, 97, 112, 100, 101, 116, 101, 77, 78, 71, 72, 87, 89, 90, 99, 102, 131, 105, 96, 99, 107, 108, 155, 129, 159, 138, 131, 132, 147
Offset: 1

Views

Author

Juri-Stepan Gerasimov, May 17 2010

Keywords

Links

Crossrefs

Cf. A001358, A122466.

Programs

  • Mathematica
    #-Length[Permutations[IntegerDigits[#,2]]]&/@Select[Range[ 2,300], PrimeOmega[ #] == 2&] (* Harvey P. Dale, Jun 21 2014 *)

Formula

a(n)=s-binomial((A000120(s)+A023416(s)), A000120(s)), where s=semiprime(n).

Extensions

More terms from R. J. Mathar, May 28 2010

A122613 Integers 1 through n written in primorial base, summed as if decimal.

Original entry on oeis.org

1, 11, 22, 42, 163, 264, 374, 485, 605, 726, 926, 1127, 1337, 1548, 1768, 1989, 2289, 2590, 2900, 3211, 3531, 3852, 4252, 4653, 5063, 5474, 5894, 6315, 7315, 8316, 9326, 10337, 11357, 12378, 13478, 14579, 15689, 16800, 17920, 19041, 20241, 21442
Offset: 1

Views

Author

Jonathan Vos Post, Sep 20 2006

Keywords

Comments

cf. A049345 n written in primorial base [Places reading from right have values (1, 2, 6, 30, 210, ...) = primorials]. Primes in this sequence are a(2) = 11, a(6) = 163, a(33) = 10337.

Examples

			a(1) = A049345(1) = 1.
a(2) = A049345(1) + A049345(2) = 1 + 10 = 11.
a(3) = A049345(1) + A049345(2) + A049345(3) = 1 + 10 + 11 = 22.
a(4) = 1 + 10 + 11 + 20 = 42.
a(5) = 1 + 10 + 11 + 20 + 21 = 63.
a(6) = 1 + 10 + 11 + 20 + 21 + 100 = 163.
a(33) = 1 + 10 + 11 + 20 + 21 + 100 + 101 + 110 + 111 + 120 + 121 + 200 + 201 + 210 + 211 + 220 + 221 + 300 + 301 + 310 + 311 + 320 + 321 + 400 + 401 + 410 + 411 + 420 + 421 + 1000 + 1001 + 1010 + 1011 = 10337.

Crossrefs

Cf. Primorials: A002110, factorial base A007623, A000040, A001358, A007088, A004676, A020767, A038506, A067894, A067895, A121718, A122466, A122467.
Showing 1-3 of 3 results.

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