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.

A134070 Primes in A130774.

Original entry on oeis.org

13, 13471118294776123, 134711182947761231993225218431364220735715778934915127244763960364079103682167761271443439204710647114985118604983010349
Offset: 1

Views

Author

Alexander Adamchuk, Oct 06 2007

Keywords

Comments

A130774 = {1, 13, 134, 1347, 134711, 13471118, 1347111829, 134711182947, 13471118294776, 13471118294776123, ...} = Concatenate Lucas numbers. Indices of prime terms in A130774 are {2, 10, 31, ...}.
a(4) > A130774(500) = 1.347...*10^26425, if it exists. - Amiram Eldar, Jul 17 2025

Examples

			a(1) = A130774(2) = 13.
a(2) = A130774(10) = 13471118294776123.
a(3) = A130774(31) = 13471118294776123199322521843136422073571577893491512724476396036407910368216776127144343920471064711498511860498301034.

Links

Crossrefs

Cf. A000204 (Lucas numbers).
Cf. A130774 (concatenation of Lucas numbers).
Cf. A019523 (concatenation of Fibonacci numbers).
Cf. A038399 (concatenation of first n nonzero Fibonacci numbers in reverse order).
Cf. A134072 (concatenation of A000204 Lucas numbers (beginning at 1) in reverse order).
Cf. A134069 (primes in A038399).
Cf. A134071 (primes in A134072).

Programs

  • Mathematica
    Select[Module[{nn=40,ll},ll=LucasL[Range[nn]];Table[FromDigits[Flatten[IntegerDigits/@Take[ll,n]]],{n,nn}]],PrimeQ] (* Harvey P. Dale, May 07 2023 *)

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

A134072 Concatenation of A000204 Lucas numbers (beginning at 1) in reverse order.

Original entry on oeis.org

1, 31, 431, 7431, 117431, 18117431, 2918117431, 472918117431, 76472918117431, 12376472918117431, 19912376472918117431, 32219912376472918117431, 52132219912376472918117431, 84352132219912376472918117431
Offset: 1

Views

Author

Alexander Adamchuk, Oct 06 2007

Keywords

Comments

Indices of prime terms are {2, 3, 5, 11, ...}. Primes are listed in A134071 = {31, 431, 117431, 19912376472918117431, ...}.

Links

Crossrefs

Cf. A000204 (Lucas numbers).
Cf. A130774 (concatenation of Lucas numbers).
Cf. A019523 (concatenation of Fibonacci numbers).
Cf. A038399 (concatenation of first n nonzero Fibonacci numbers in reverse order).
Cf. A134069 (primes in A038399).
Cf. A134070 (primes in A130774).
Cf. A134071 (primes in A134072).

Programs

  • Mathematica
    Module[{nn=20,lnos},lnos=LucasL[Range[nn]];Table[FromDigits[Flatten[ IntegerDigits/@ Reverse[Take[lnos,n]]]],{n,nn}]] (* Harvey P. Dale, Jul 27 2015 *)

Extensions

Edited by Charles R Greathouse IV, Apr 26 2010

A134071 Primes in A134072.

Original entry on oeis.org

31, 431, 117431, 19912376472918117431
Offset: 1

Views

Author

Alexander Adamchuk, Oct 06 2007

Keywords

Comments

A134072 = {1, 31, 431, 7431, 117431, 18117431, 2918117431, 472918117431, 76472918117431, 12376472918117431, 19912376472918117431, ...} = concatenation of Lucas numbers in reverse order. Indices of prime terms in A134072 are {2, 3, 5, 11, ...}.
No further terms through 500 Lucas numbers. - Harvey P. Dale, Aug 17 2013

Examples

			a(1) = A134072(2) = 31.
a(2) = A134072(3) = 431.
a(3) = A134072(5) = 117431.

Links

Crossrefs

Cf. A000204 (Lucas numbers).
Cf. A130774 (concatenation of Lucas numbers).
Cf. A019523 (concatenation of Fibonacci numbers).
Cf. A038399 (concatenation of first n nonzero Fibonacci numbers in reverse order).
Cf. A134072 (concatenation of A000204 Lucas numbers (beginning at 1) in reverse order).
Cf. A134069 (primes in A038399).
Cf. A134070 (primes in A130774).

Programs

  • Mathematica
    nn=500;With[{lucs=LucasL[Range[nn]]},Select[Table[FromDigits[ Flatten[ IntegerDigits/@ Reverse[ Take[lucs,n]]]],{n,nn}],PrimeQ]] (* Harvey P. Dale, Aug 17 2013 *)

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

A131698 Cumulative concatenation of A000032 Lucas numbers (beginning at 2).

Original entry on oeis.org

2, 21, 213, 2134, 21347, 2134711, 213471118, 21347111829, 2134711182947, 213471118294776, 213471118294776123, 213471118294776123199, 213471118294776123199322, 213471118294776123199322521
Offset: 1

Views

Author

Jonathan Vos Post, Sep 15 2007

Keywords

Comments

This is to A000032 as A130774 is to A000204. Like these Lucas numbers, a(n) cycles even, odd, odd, even, odd, odd, ... a(n) is prime for n = 1, 5 and semiprime for n = 2, 3, 6, 14. No more prime nor semiprime values through n = 60, which has a 381 digit composite factor.

Examples

			Table of first 14 values, with factorizations:
n a(n) factors
1 2 prime
2 21 3 * 7 semiprime
3 213 3 * 71 semiprime
4 2134 2 * 11 * 97
5 21347 is prime
6 2134711 719 * 2969 semiprime
7 213471118 = 2 * 7 * 19 * 802523
8 21347111829 = 3 * 12743 * 558401
9 2134711182947 = 7 * 491 * 621097231
10 213471118294776 = 2^3 * 3^2 * 41 * 7349 * 9839987
11 213471118294776123 = 3 * 41 * 785903 * 2208335567
12 213471118294776123199 = 11 * 23 * 349 * 2417648598420967
13 213471118294776123199322 = 2 * 23 * 37 * 3929 * 6991 * 4566234789049
14 213471118294776123199322521 = 61950375139 * 3445840607353939 semiprime.

Crossrefs

Cf. A000032, A000204, A130774.

Formula

a(1) = 2; a(n+1) = Concatenate(a(n),A000032(n+1)).
Showing 1-4 of 4 results.

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