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 1-5 of 5 results.

A169798 a(n) = smallest prime number > a(n-1) that contains the n-th composite number as a substring.

Original entry on oeis.org

41, 61, 83, 89, 101, 127, 149, 151, 163, 181, 1201, 1213, 1223, 1249, 1259, 2267, 2273, 2281, 2309, 3203, 3301, 3343, 3359, 3361, 3389, 3391, 3407, 4201, 4409, 4451, 4463, 4481, 4493, 4507, 4513, 4523, 4547, 5501, 5563, 5573, 5581, 6007, 6203, 6263, 6421
Offset: 1

Views

Author

N. J. A. Sloane, May 15 2010

Keywords

Links

Crossrefs

Cf. A144565.
Cf. A177981, A177982. [From Reinhard Zumkeller, May 16 2010]

Extensions

Corrected and extended by Zak Seidov and D. S. McNeil, May 16 2010

A177981 a(n) = prime number > a(n-1) that contains the n-th prime as a substring.

Original entry on oeis.org

23, 31, 53, 67, 113, 131, 173, 191, 223, 229, 311, 337, 419, 431, 479, 653, 659, 661, 673, 719, 733, 797, 839, 1289, 1297, 5101, 7103, 10709, 10903, 11113, 11273, 11311, 13709, 13901, 14149, 15101, 15727, 16301, 16703, 17317, 17903, 18119, 18191
Offset: 1

Views

Author

Reinhard Zumkeller, May 16 2010

Keywords

Examples

			.. prime(n): 2_ 3_ 5_ _7 11_ 13_ 17_ 19_ _23 _29 31_ _37
...... a(n): 23 31 53 67 113 131 173 191 223 229 311 337 .

Crossrefs

Cf. A144565, A169798, A177982.

A177982 a(n) = composite number > a(n-1) that contains the n-th composite as a substring.

Original entry on oeis.org

14, 16, 18, 39, 100, 112, 114, 115, 116, 118, 120, 121, 122, 124, 125, 126, 270, 280, 300, 320, 330, 334, 335, 336, 338, 339, 340, 342, 344, 345, 346, 348, 490, 500, 510, 520, 540, 550, 556, 570, 580, 600, 620, 630, 640, 650, 660, 668, 669, 670, 672, 674
Offset: 1

Views

Author

Reinhard Zumkeller, May 16 2010

Keywords

Comments

a(n) <= 10*n.

Examples

			.. comp(n): _4 _6 _8 _9 _10 _12 _14 _15 _16 _18 _20 _21
..... a(n): 14 16 18 39 100 112 114 115 116 118 120 121 .

Crossrefs

Cf. A169798, A144565, A177981.

A178057 Smallest prime number > a(n-1) that contains the n-th semiprime number as a substring.

Original entry on oeis.org

41, 61, 79, 101, 149, 151, 211, 223, 251, 263, 331, 347, 353, 383, 397, 461, 491, 751, 1553, 1571, 1583, 1621, 1657, 1669, 1741, 1777, 1823, 2851, 2861, 2879, 2917, 2939, 3943, 4951, 10601, 11113, 11159, 11801, 11903, 12101, 12203, 12301, 12907, 13309
Offset: 1

Views

Author

Jonathan Vos Post, May 18 2010

Keywords

Comments

Not to be confused with smallest semiprime number > a(n-1) that contains the n-th prime number as a substring. This is the 2nd row of an infinite array A[k,n] = Smallest k-almost prime number > a(n-1) that contains the n-th prime number as a substring. This is one plane of the infinite 3-D array A[j,k,n] = Smallest k-almost prime number > a(n-1) that contains the n-th prime number as a substring in base j representation.

Examples

			a(1) = 41 because 41 is the smallest prime whose decimal representation has "4" as a substring, and 4 = 2*2 is the 1st (smallest) semiprime (number of the form p*q where p and q are primes, not necessarily distinct).
a(2) = 61 because 61 is the smallest prime whose decimal representation has "6" as a substring, and 6 = 2*3 is the 2nd semiprime.
a(3) = 79 because 79 is the smallest prime > 61 whose decimal representation has "9" as a substring, and 9 = 3*3 is the 3rd semiprime.

Crossrefs

Cf. A000040, A001358, A144565, A169798.

Formula

a(n) = MIN{p > a(n-1) in A000040 such that A001358(n) as a string of decimal digits is a substring of p as a string of decimal digits}.

Extensions

Edited, corrected and extended by Ray Chandler, May 23 2010

A173716 Smallest number that contains the first n semiprimes as substrings.

Original entry on oeis.org

4, 46, 469, 10469, 101469, 10141569, 101421569, 1014221569, 101421522569, 1014215225269, 101421522526339, 1014215225263349, 101421522526334359, 10142152252633435389, 101421522526334353839, 1014215225263346353839
Offset: 1

Views

Author

N. J. A. Sloane, Nov 25 2010

Keywords

Comments

Semiprime analog of A054261.

References

  • Jonathan Vos Post, Posting to the Sequence Fans Mailing List, May 24 2010

Crossrefs

Cf. A000040, A001358, A054260, A035239, A178057, A144565, A169798.

Extensions

More terms from Sean A. Irvine, Dec 02 2010
Showing 1-5 of 5 results.

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

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