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 1-4 of 4 results.

A166504 Slime numbers: numbers which are the concatenation of primes, with "leading zeros" allowed.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 112, 113, 115, 117, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 175, 177, 179
Offset: 1

Views

Author

M. F. Hasler, Nov 02 2009

Keywords

Comments

A number is in this sequence if and only if it is prime or of the form a(k)*10^m+a(n), where a(k), a(n) are in this sequence and 10^m >= a(n) (and from this follows that one among a(k), a(n) can be taken to be prime).
This contains A152242 as a subsequence, but also additional terms like e.g. 202 which can be split into two primes, 2 and 02 (= 2). Such a splitting, where some of the substrings contain leading zeros, is not allowed in A152242.
Terms not in A152242 are listed in A166505.

Links

Crossrefs

Cf. A152242 (no leading zeros allowed).
Cf. A085823 (super-slimes: all substrings are prime). - Henri Picciotto, Apr 01 2015

Programs

  • PARI
    is_A166504(n)={ isprime(n) || ((bittest(n,0) || n%10==2) & for(i=1,#Str(n)-1, isprime(n%10^i) & is_A166504(n\10^i) & return(1)))}
  • PARI
    is(n)=if(isprime(n),return(1));if(n<202,return(isprime(n%10)&&isprime(n\10)));my(k=n%10,v);if(k==5||k==2,return(if(n<6,1,n\=10;has(n/10^valuation(n,10)))));if(k%2==0,return(0));v=digits(n);for(i=1,#v,if(isprime(n%10^i)&&is(n\10^i),return(1)));0 \\ Charles R Greathouse IV, Apr 30 2013

Extensions

Edited by Charles R Greathouse IV, Apr 23 2010
Name "Slime numbers", after Henri Picciotto, added by N. J. A. Sloane, Mar 25 2015

A167459 Composite numbers in A166504, i.e., whose decimal expansion can be split up into prime numbers, with leading zeros allowed.

Original entry on oeis.org

22, 25, 27, 32, 33, 35, 52, 55, 57, 72, 75, 77, 112, 115, 117, 132, 133, 135, 172, 175, 177, 192, 195, 202, 203, 205, 207, 213, 217, 219, 222, 225, 231, 232, 235, 237, 243, 247, 252, 253, 255, 259, 261, 267, 272, 273, 275, 279, 289, 292, 295, 297, 302, 303
Offset: 1

Views

Author

M. F. Hasler, Nov 19 2009

Keywords

Comments

In contrast to A066737 (which is a subsequence of this one), we allow for leading zeros in the "prime" substrings; the two sequences differ from n=24 on, with a(24)=202 which is not in A066737.
Sequence A166505 gives the difference, A167459 \ A066737 = A166504 \ A152242. Sequence A167458 gives the indices of the terms not in A066737.

Crossrefs

Cf. A002808, A066737, A121609, A166504, A167505.

Programs

Formula

A167459 = A002808 n A166504, where "n" means intersection.
A167459 \ A066737 = A166504 \ A152242.

A166506 Indices of terms in A166504 which are not in A152242.

Original entry on oeis.org

70, 71, 72, 73, 115, 116, 117, 183, 185, 186, 250, 251, 252, 253, 365, 367, 368, 427, 429, 534, 535, 536, 537, 594, 595, 596, 640, 642, 643, 645, 647, 648, 649, 650, 653, 654, 655, 656, 657, 659, 660, 661, 662, 664, 665, 666, 667, 669, 671, 672, 673, 674
Offset: 1

Views

Author

M. F. Hasler, Nov 02 2009

Keywords

Examples

			a(1)=70 since the first term in A166504 which is not in A152242 is A166504(70)=202.

Crossrefs

Cf. A152242, A166504, A166505.

Programs

  • PARI
    c=0; for(i=1,1e4, is_A166504(i) & c++ & !is_A152242(i) & print1(c", "))

Formula

A166504(a(n)) = A166505(n).

A167458 Indices of numbers in A167459 which are not in A066737.

Original entry on oeis.org

24, 25, 26, 27, 53, 54, 55, 88, 89, 90, 124, 125, 126, 127, 181, 182, 183, 215, 216, 268, 269, 270, 271, 303, 304, 305, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364
Offset: 1

Views

Author

M. F. Hasler, Nov 19 2009

Keywords

Comments

Also, indices of terms in A167459 which are in A166505 (or: which are not in A152242).

Crossrefs

Cf. A166504, A152242.

Programs

  • PARI
    c=0; for(n=1,9999, is_A167459(n) & c++ & !is_A152242(n) & print1(c", "))
Showing 1-4 of 4 results.

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

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