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.

User: Karl Hovekamp

Karl Hovekamp's wiki page.

Karl Hovekamp has authored 7 sequences.

A180641 Primes P such that P > (largest prime factor of (P-1)) * (largest prime factor of (P+1)).

Original entry on oeis.org

7, 17, 19, 31, 41, 53, 71, 79, 89, 97, 101, 109, 127, 151, 163, 181, 191, 197, 199, 239, 241, 251, 257, 271, 307, 337, 349, 379, 401, 419, 431, 433, 449, 461, 463, 487, 491, 499, 521, 571, 577, 593, 599, 601, 631, 641, 647, 659, 683, 701, 727, 751, 769, 809
Offset: 1

Views

Author

Karl Hovekamp, Sep 14 2010

Keywords

Examples

			Example: For n = 3, a(3)=19.
The prime P = 19
P-1 = 18 (largest prime factor of 18 is 3)
P+1 = 20 (largest prime factor of 20 is 5)
19 > 3*5.

Links

Crossrefs

Cf. A180640. See also A103666, A103667.

Programs

  • Mathematica
    lpfQ[n_]:=Module[{a=FactorInteger[n-1][[-1,1]],b=FactorInteger[n+1][[-1,1]]},n>a*b]; Select[Prime[Range[200]],lpfQ] (* Harvey P. Dale, Aug 16 2013 *)
  • PARI
    lpf(n) = {f = factor(n); return (f[#f~, 1]);}
lista(nn) = {forprime(p=3, nn,if ((p > lpf(p-1)*lpf(p+1)), print1(p, ", ");););} \\ Michel Marcus, Jul 25 2013

A180640 Primes P such that P < (largest prime factor of (P-1)) * (largest prime factor of (P+1)).

Original entry on oeis.org

2, 3, 5, 11, 13, 23, 29, 37, 43, 47, 59, 61, 67, 73, 83, 103, 107, 113, 131, 137, 139, 149, 157, 167, 173, 179, 193, 211, 223, 227, 229, 233, 263, 269, 277, 281, 283, 293, 311, 313, 317, 331, 347, 353, 359, 367, 373, 383, 389, 397, 409, 421, 439, 443, 457, 467
Offset: 1

Views

Author

Karl Hovekamp, Sep 14 2010

Keywords

Examples

			For n = 3, a(3)=11.
The prime P = 11
P-1 = 10 (largest prime factor of 10 is 5)
P+1 = 12 (largest prime factor of 12 is 3)
11 < 5*3.

Crossrefs

Cf. A180641. See also A103666, A103667.

Programs

  • Mathematica
    Select[Prime[Range[100]],#<(FactorInteger[#-1][[-1,1]] FactorInteger[#+1][[-1,1]])&]  (* Harvey P. Dale, Feb 22 2011 *)
  • PARI
    isok(p) = (p==2) || (isprime(p) && (p < vecmax(factor(p-1)[, 1]) * vecmax(factor(p+1)[, 1]))); \\ Michel Marcus, Oct 29 2022

Extensions

Initial term, i.e., 2, added by Harvey P. Dale, Feb 22 2011

A173619 Differences between consecutive pseudoprimes to base 2.

Original entry on oeis.org

220, 84, 460, 282, 342, 176, 142, 418, 236, 120, 456, 756, 336, 2, 310, 780, 1140, 1356, 364, 160, 430, 1350, 324, 720, 1496, 940, 6, 234, 510, 1218, 132, 864, 2000, 16, 1230, 3050, 376, 2384, 3580, 780
Offset: 1

Views

Author

Karl Hovekamp, Feb 22 2010

Keywords

Comments

These are the differences between the numbers in sequence A001567.

Examples

			341, 561, 645, 1105, .... (sequence A001567)
abs(341-561)=220
abs(561-645)=84
abs(645-1105)=460
....

Links

Crossrefs

Cf. A001567.

A138329 List of strictly non-palindromic twin primes {p, p+2}.

Original entry on oeis.org

137, 139, 4337, 4339, 8291, 8293, 9419, 9421, 10937, 10939, 13757, 13759, 19427, 19429, 20981, 20983, 36011, 36013, 38327, 38329, 43397, 43399, 59441, 59443, 71327, 71329, 74717, 74719, 76871, 76873, 90437, 90439, 91571, 91573, 117239
Offset: 1

Views

Author

Karl Hovekamp, Mar 14 2008

Keywords

Comments

The strictly non-palindromic twin primes are a part of the normal twin primes. See the list of twin primes A077800 and A016038 for the strictly non-palindromic numbers.

References

  • Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

Links

Crossrefs

Cf. A016038, A047811, A016038, A077800, A099609.

Formula

Twin primes, where both numbers {p} and {p+2} are strictly non-palindromic.

A138358 List of triples of strictly non-palindromic primes without an ordinary prime in between.

Original entry on oeis.org

137, 139, 149, 1433, 1439, 1447, 4337, 4339, 4349, 5297, 5303, 5309, 8287, 8291, 8293, 13049, 13063, 13093, 30293, 30307, 30313, 36007, 36011, 36013, 43391, 43397, 43399
Offset: 1

Views

Author

Karl Hovekamp, Mar 16 2008

Keywords

Comments

Up to 10^9 there are 2992 triples of strictly non-palindromic primes if the quadruples and quintuples are not counted.
For quadruples of this kind, see A138359.
For quintuples of this kind, see A138360.

Examples

			Primes:
...
113 is palindromic in base 8
127 is palindromic in base 2 and base 9
131 is palindromic in base 10
137 is strictly non-palindromic
139 is strictly non-palindromic
149 is strictly non-palindromic
151 is palindromic in base 3 and base 10
157 is palindromic in base 7 and base 12
...
So {137, 139, 149} is the first triple of strictly non-palindromic primes.

References

  • Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

Links

Crossrefs

Cf. A138359, A138360, A138329, A016038, A047811, A016038.

Formula

A small fraction of the primes are strictly non-palindromic. Notice that all strictly non-palindromic numbers >6 are prime! (see: A016038) Triples of these strictly non-palindromic primes, without any normal prime in between, are listed here.

A138359 List of quadruples of strictly non-palindromic primes without an ordinary prime in between them.

Original entry on oeis.org

44449, 44453, 44483, 44491, 120811, 120817, 120823, 120829, 315037, 315047, 315059, 315067, 583069, 583087, 583127, 583139, 617411, 617429, 617447, 617453, 1553423, 1553429, 1553437, 1553467, 1712329, 1712339, 1712353, 1712369
Offset: 1

Views

Author

Karl Hovekamp, Mar 16 2008

Keywords

Comments

For triples of this kind, see A138358.
For quintuples of this kind, see A138360.

Examples

			Primes:
...
44417 palindromic in bases 50, 106, 135 and 141
44449 strictly non-palindromic
44453 strictly non-palindromic
44483 strictly non-palindromic
44491 strictly non-palindromic
44497 palindromic in base 67 and base 206
...
So {44449, 44453, 44483, 44491} is the first quadruple of strictly non-palindromic primes.

References

  • Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

Links

Crossrefs

Cf. A138358, A138360, A138329, A016038, A047811, A016038.

A138360 Quintuples of 5 consecutive strictly non-palindromic primes.

Original entry on oeis.org

3253177, 3253219, 3253223, 3253231, 3253241, 20189111, 20189119, 20189123, 20189137, 20189167, 22122937, 22122979, 22122983, 22123021, 22123043, 61309069, 61309081, 61309091, 61309093, 61309097, 89073521, 89073533, 89073583, 89073599, 89073613
Offset: 1

Views

Author

Karl Hovekamp, Mar 16 2008

Keywords

Comments

The quintuples T(n,1), T(n,2), .. T(n,5), n>=1, in this array are 5 consecutive primes (consecutive in A000040) which are also members of A016038.
Notice that all strictly non-palindromic numbers >6 are prime! (See A016038.) Quintuples of these strictly non-palindromic primes, without any normal prime in between, are listed here.
Up to 1 billion there are only 5 quintuples of strictly non-palindromic primes. May be that there are no more quintuples of this kind. Up to 1 billion there are no n-tuples of strictly non-palindromic primes with n>5.

Examples

			Primes:
...
3253153 palindromic in bases 203, 356, 495, 1316, 1442, 1504 and 1648
3253177 strictly non-palindromic
3253219 strictly non-palindromic
3253223 strictly non-palindromic
3253231 strictly non-palindromic
3253241 strictly non-palindromic
3253253 palindromic in bases 653, 768, 910 and 1001
...
So {3253177, 3253219, 3253223, 3253231, 3253241} is the first quintuple of the strictly non-palindromic primes.

References

  • Karl Hovekamp, Palindromzahlen in adischen Zahlensystemen, 2004

Links

Crossrefs

Cf. A138358 (triples), A138359 (4-tuples), A138329, A016038, A047811, A016038.

Extensions

More terms from Mauro Fiorentini, Jan 03 2016

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