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.

A145531 Primes p mentioned in A155214.

Original entry on oeis.org

2, 3, 71, 97, 103, 331, 4091, 5879, 7207, 7639, 17123, 17383, 20809, 46889, 47363, 139493, 142969, 150869, 154111, 154753, 155663, 162419, 165059, 166739, 174893, 179989, 184273, 190759, 197311, 199909, 270527, 280613
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jan 22 2009, Mar 02 2009, Mar 04 2009

Keywords

Links

Programs

  • Mathematica
    palQ[n_] := Reverse[x = IntegerDigits[n]] == x; Select[Prime[Range[25000]], palQ[# + Prime[#]] &] (* Jayanta Basu, Jun 24 2013 *)

A176465 Palindromic primes p(k) = palprime(k) such that their sum of digits ("sod") equals sum of digits of their palprime index k.

Original entry on oeis.org

13331, 1022201, 1311131, 3001003, 3002003, 100707001, 102272201, 103212301, 103323301, 103333301, 104111401, 105202501, 105313501, 105323501, 106060601, 111181111, 111191111, 112494211, 121080121, 140505041, 160020061, 160161061
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 18 2010

Keywords

Comments

p(k) = palprime(k) (see A002385) with sod(p(k)) = sod(k)
List of (p(k),k):
(13331,29) (1022201,116) (1311131,173) (3001003,304) (3002003,305)
(100707001,790) (102272201,818) (103212301,832) (103323301,835) (103333301,836)
(104111401,850) (105202501,862) (105313501,865) (105323501,866) (106060601,875)
(111181111,961) (111191111,962) (112494211,979) (121080121,1096) (140505041,1379)
(160020061,1672) (160161061,1678) (160171061,1679) (181111181,1958) (300151003,2209)
(310131013,2344) (313222313,2387) (320444023,2488) (321242123,2495) (341040143,2765)
(341222143,2767) (342020243,2774) (342202243,2776) (342212243,2777) (342313243,2779)
(343050343,2788) (700090007,3488) (730111037,3884) (910212019,4858)

Examples

			p(1) = 13331 = palprime(29), sod(p(1)) = 1+3+3+3+1 = 11 = sod(29), first term
p(8) = 103212301 = palprime(832), sod(p(8)) = 1+0+3+2+1+2+3+1 = 13 = 8+3+2 = sod(832), 8th term
p(?) = 156300010003651 = palprime(99643), sod(p(?)) = 31 = sod(99733)
Note successive p(i) and p(i+1) which are also consecutive palindromic primes (i = 4, 9, 13, 16, 22, 33)

References

  • A. H. Beiler: Recreations in the Theory of Numbers: The Queen of Mathematical Entertains. Dover Publications, New York, 1964
  • M. Gardner: Mathematischer Zirkus , Ullstein Berlin-Frankfurt/Main-Wien, 1988
  • K. G. Kroeber: Ein Esel lese nie. Mathematik der Palindrome, Rowohlt Tb., Hamburg, 2003

Crossrefs

A000213, A002385, A033548, A155214, A176111

A174884 Palindromic primes using only (decimal) square digits 0,1,4,9.

Original entry on oeis.org

11, 101, 191, 919, 11411, 19991, 91019, 94049, 94949, 1114111, 1190911, 1409041, 1411141, 1444441, 1490941, 1909091, 1941491, 9049409, 9091909, 9109019, 9110119, 9149419, 9199919, 9400049, 9414149, 9419149, 9440449, 9919199
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 01 2010

Keywords

Comments

Four decimal square digits: 0 = 0^2, 1 = 1^2, 4 = 2^2, 9 = 3^2
With the exception of 11 all palindromic primes have an odd number of digits

Examples

			11 = prime(5) = palprime(5), 1st term of sequence.
101 = prime(26) = palprime(6), 2nd term of sequence.
Next term using only 0 and 1 is 100111001 = prime(5767473) = palprime(785).

References

  • Roland Sprague, Unterhaltsame Mathematik, neue Probleme, ueberraschende Loesungen, Vieweg, Braunschweig, 1961
  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books: London, 1986.

Links

Crossrefs

Cf. A002385, A007500, A083185, A155214.

Programs

  • Mathematica
    Select[FromDigits/@Tuples[{0,1,4,9},7],PalindromeQ[#]&&PrimeQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 06 2019 *)

A178654 Palindromic primes of the form (q//R(q))/11 where q is an emirp, R() denotes digit-reversal and // concatenation.

Original entry on oeis.org

727, 10301, 14341, 16361, 18181, 30703, 1003001, 1145411, 1163611, 1201021, 1363631, 1452541, 3001003, 3425243, 3503053, 100030001, 102343201, 103212301, 105272501, 105343501, 107070701, 107121701, 112030211, 124525421, 125010521
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jun 01 2010

Keywords

Comments

Concatenation of the emirps q (A006567) and their digit-reversed variant yields the sequence q//R(q) = 1331, 1771, 3113, 3773, 7117, 7337, 7997,..
Further division of each term through 11 (in the spirit of A132286) yields the sequence 121, 161, 283, 343, 647, 667, 727, 889, 9791..
If such a term is a palindromic prime (A002385), it joins the sequence.
The sequence is generated by the emirps A006567(i) with i= 7, 10, 12, 14, 15, 17, 45, 59, 60, 63, 72, 77, 115, 139, 143, 280, 289,...

Examples

			79 = emirp(7), 97 = emirp(8), 7997 / 11 = 727 = palprime(15) is first term
113 = emirp(10), 311 = emirp(16), 113311 / 11 = 10301 = palprime(21) is 2nd term
14303 = emirp(414), 30341 = emirp(639), 1430330341 / 11 = 130030031 = palprime(1229), 26th term

References

  • M. Gardner: Mathematischer Zirkus, Seite 259 ff., Ullstein Berlin-Frankfurt/M.-Wien, 1988
  • W. Lietzmann: Sonderlinge im Reich der Zahlen, Duemmler, Bonn, 1948

Links

Crossrefs

Cf. A002385, A006567, A155214
Showing 1-4 of 4 results.

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