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.

A108810 Self-describing primes.

Original entry on oeis.org

10153331, 10173133, 10233221, 10311533, 10322321, 12103331, 12163133, 12163331, 12193133, 12311933, 12313319, 15103133, 15233221, 15311633, 15331931, 15333119, 16153133, 16153331, 16173133, 16331531, 16331831, 16333117, 17143331, 17311633, 17331031, 18103133
Offset: 1

Views

Author

G. L. Honaker, Jr., Jul 12 2005

Keywords

Comments

Self-descriptive numbers are read in pairs of digits.
This uses a different method from A047841. Here the digits are described in any order, whereas in A047841 they must be described in increasing order.

Examples

			E.g. 10153331 reads "One 0, one 5, three 3's and three 1's", which does indeed describe 10153331.

References

  • Computed by Jud McCranie.
  • Mudge, 'Numbers Count', Personal Computer World, Jun 15 1996

Links

Crossrefs

Cf. A047841, A059504, A109775, A109776, A173101.

Extensions

More terms from Giovanni Resta, Aug 14 2019

A173101 Self-describing semiprimes.

Original entry on oeis.org

22, 10183133, 10183331, 10213223, 10313317, 10322123, 10331831, 10331931, 10333117, 12183133, 12183331, 12193331, 12311033, 12311633, 12311833, 12313318, 12331031, 12333115, 12333119, 14103331, 14153331, 14163133, 14173133, 14183133, 14193331, 14311533, 14311633
Offset: 1

Views

Author

Jonathan Vos Post, Feb 09 2010

Keywords

Comments

This is to A001358 as A108810 is to A000040.

Examples

			a(1) = 22 because "22" does indeed consist of "two 2's" and 22 = 2 * 11 is semiprime. a(4) = 10213223 because 10213223 consists of one "0", two 1's, three 2's, and two 3's; and 10213223 = 41 * 249103 is semiprime.

Links

Crossrefs

Cf. A001358, A108810, A109776.

Formula

{A109776 INTERSECTION A001358}. a(n) = n-th integer k such that OMEGA(k)=2 where OMEGA(n) is the sum of the exponents in the prime decomposition of k, and reading the number (in base 10) in successive pairs of digits gives a (possibly redundant) description of the number.

Extensions

More terms from Giovanni Resta, Aug 14 2019

A173095 Partial sums of A108810.

Original entry on oeis.org

10153331, 20326464, 30559685, 40871218, 51193539, 63296870, 75460003, 87623334, 99816467, 112128400, 124441719, 139544852, 154778073, 170089706, 185421637, 200754756, 216907889, 233061220, 249234353, 265565884, 281897715
Offset: 1

Views

Author

Jonathan Vos Post, Feb 09 2010

Keywords

Comments

Partial sums of self-describing primes, where the digits are described in any order, whereas in A047841 they must be described in increasing order. The subsequence of prime partial sums of self-describing primes begins: 10153331, 75460003. What is the smallest value in the subsubsequence of self-describing prime partial sums of self-describing primes?

Examples

			a(7) = 10153331 + 10173133 + 10233221 + 10311533 + 10322321 + 12103331 + 12163133 = 75460003 is prime. a(21) = 10153331 + 10173133 + 10233221 + 10311533 + 10322321 + 12103331 + 12163133 + 12163331 + 12193133 + 12311933 + 12313319 + 15103133 + 15233221 + 15311633 + 15331931 + 15333119 + 16153133 + 16153331 + 16173133 + 16331531 + 16331831.

Links

Crossrefs

Cf. A000040, A047841, A059504, A108810, A109775, A109776.

Formula

a(n) = SUM[i=1..n] A108810(i).
Showing 1-3 of 3 results.

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

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