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 1-6 of 6 results.

A133019 Product of n-th prime and n-th prime written backwards.

Original entry on oeis.org

4, 9, 25, 49, 121, 403, 1207, 1729, 736, 2668, 403, 2701, 574, 1462, 3478, 1855, 5605, 976, 5092, 1207, 2701, 7663, 3154, 8722, 7663, 10201, 31003, 75007, 98209, 35143, 91567, 17161, 100147, 129409, 140209, 22801, 117907, 58843, 127087
Offset: 1

Views

Author

Omar E. Pol, Oct 27 2007

Keywords

Comments

a(8) = 1729 is the second taxicab number, also called the Hardy-Ramanujan number (see A001235, A011541 and A133029).

Examples

			a(8) = 1729 because the 8th prime is 19 and 19 written backwards is 91 and 19*91 = 1729.

Links

Crossrefs

Cf. A001235, A004087, A011541, A061205, A067563, A067087, A133029. Prime numbers: A000040.

Programs

  • Mathematica
    #*FromDigits[Reverse[IntegerDigits[#]]] & /@ Prime[Range[1, 50]] (* G. C. Greubel, Oct 02 2017 *)
#*IntegerReverse[#]&/@Prime[Range[40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 29 2021 *)
  • PARI
    vector(60, n, prime(n)*subst(Polrev(digits(prime(n))), x, 10)) \\ Michel Marcus, Dec 17 2014

Formula

a(n) = A000040(n) * A004087(n)

A066492 a(n) = A056524(n)/11.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181, 182, 192, 202, 212, 222, 232, 242, 252, 262, 272, 273, 283, 293, 303, 313, 323, 333, 343, 353, 363, 364, 374, 384, 394, 404, 414, 424, 434, 444, 454, 455, 465, 475, 485, 495, 505, 515
Offset: 1

Views

Author

Vladeta Jovovic, Jan 09 2002

Keywords

Crossrefs

Cf. A056524, A067087, A071272.

Extensions

Edited by N. J. A. Sloane at the suggestion of Artur Jasinski, Aug 24 2007

A088883 Primes which when concatenated with their reverse and incremented by 2 yield a new prime.

Original entry on oeis.org

7, 19, 97, 109, 151, 163, 181, 193, 547, 709, 727, 733, 991, 1039, 1093, 1279, 1447, 1453, 1567, 1621, 1657, 1669, 1699, 1723, 1867, 5077, 5179, 5209, 5281, 5323, 5419, 5503, 5563, 5581, 5653, 5821, 5857, 5881, 7057, 7207, 7219, 7333, 7351, 7507, 7537
Offset: 1

Views

Author

Chuck Seggelin, Oct 21 2003

Keywords

Comments

It appears that if concat(p,reverse(p))+2 is prime, then concat(p,reverse(p))-2 is not and vice versa. This was tested for the first 60000 primes.
Conjecture: All these primes are of the form 6*k + 1. - Davide Rotondo, Apr 29 2025

Examples

			109 is a term because (i) 109 is prime and (ii) when 109 is concatenated with its reverse (901) + 2, the result (109903) is prime.

Links

Crossrefs

Subsequence of A002476.
Cf. A067087 (concatenation of n-th prime and its reverse), A088884 (with decremented rather than incremented).

Programs

  • Maple
    filter:= proc(n) local L,d,i,x;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  d:= nops(L);
  x:= add(L[-i]*(10^(i-1)+10^(2*d-i)),i=1..d)+2;
  isprime(x)
end proc;
select(filter, [seq(i,i=7 .. 10^4,6)]); # Robert Israel, Apr 29 2025
  • Mathematica
    crpQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[FromDigits[ Join[ idn, Reverse[ idn]]]+2]]; Select[Prime[Range[1000]],crpQ] (* Harvey P. Dale, Apr 28 2014 *)

A088884 Primes which when concatenated with their reverse and decremented by 2 yield a new prime.

Original entry on oeis.org

3, 5, 11, 53, 107, 131, 149, 167, 179, 191, 311, 317, 389, 503, 599, 947, 971, 1049, 1061, 1097, 1187, 1223, 1259, 1427, 1439, 1523, 1571, 1583, 1697, 1721, 1787, 1811, 1871, 1913, 1931, 1949, 3089, 3119, 3191, 3209, 3299, 3449, 3617, 3671, 3677, 3761
Offset: 1

Views

Author

Chuck Seggelin, Oct 21 2003

Keywords

Comments

It appears that if concat(p,reverse(p))-2 is prime, then concat(p,reverse(p))+2 is not and vice versa. This was tested for the first 60000 primes.
Conjecture: except for 3, all these primes are of the form 6*k - 1. - Davide Rotondo, Apr 29 2025

Examples

			53 is a term because (i) 53 is prime and (ii) when 53 is concatenated with its reverse (35) - 2, the result (5333) is prime.

Links

Crossrefs

Cf. A067087 (concatenation of n-th prime and its reverse), A088883 (with incremented rather than decremented).

Programs

  • Mathematica
    Select[Prime[Range[600]],PrimeQ[FromDigits[Join[IntegerDigits[#], Reverse[ IntegerDigits[ #]]]]- 2]&] (* Harvey P. Dale, Apr 06 2017 *)

A176597 Double primes: concatenation of the n-th prime with itself.

Original entry on oeis.org

22, 33, 55, 77, 1111, 1313, 1717, 1919, 2323, 2929, 3131, 3737, 4141, 4343, 4747, 5353, 5959, 6161, 6767, 7171, 7373, 7979, 8383, 8989, 9797, 101101, 103103, 107107, 109109, 113113, 127127, 131131, 137137, 139139, 149149, 151151, 157157, 163163
Offset: 1

Views

Author

Vincenzo Librandi, Apr 21 2010

Keywords

Examples

			Concatenation 2 and 2 is 22; 3 and 3 is 33; 5 and 5 is 55; etc.

Links

Crossrefs

Cf. A000040, A020338, A067087.

Programs

  • Magma
    [Seqint(Intseq(p) cat Intseq(p)): p in PrimesUpTo(200)]; // Vincenzo Librandi, Mar 14 2013
  • Mathematica
    dp[n_] := Module[{idn = IntegerDigits[n]}, FromDigits[Join[idn, idn]]]; dp /@ Prime[Range[40]] (* Harvey P. Dale, Jun 02 2011 *)
  • PARI
    a(n) = { my(p=Str(prime(n))); eval(concat(p,p)); } /* Joerg Arndt, Mar 14 2013 */

Extensions

Edited by Charles R Greathouse IV and R. J. Mathar, Apr 23 2010

A260874 Smallest prime of the form p//r//p//r//p//r// ...., where p = prime(n), r = A004086(p) and // denotes concatenation.

Original entry on oeis.org

1331133113, 17711771177117711771177117711771177117711771177117711771177117711771177117, 19911991199119, 23322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223322332233223, 2992299229, 31133113311331
Offset: 6

Views

Author

Felix Fröhlich, Aug 02 2015

Keywords

Links

Crossrefs

Cf. A067087, A110408.

Programs

  • PARI
    a(n) = p=prime(n); r=eval(concat(Vecrev(Str(p)))); s=eval(Str(p, r)); i=0; while(!ispseudoprime(s), if(i%2==0, s=eval(Str(s, p)); i++, s=eval(Str(s, r)); i++)); s
Showing 1-6 of 6 results.

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

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