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.

A092448 Primes in A092447.

Original entry on oeis.org

3, 53, 171311753, 8983797371676159534743413731292319171311753
Offset: 1

Views

Author

Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004

Keywords

Comments

The next term, a(5), is too large to include. - Ray Chandler, Mar 28 2004
a(5), a(6) start with 383..., 8831...: cf. A100003. - M. F. Hasler, Apr 05 2008

Crossrefs

Cf. A100003.

Programs

  • PARI
    t="";forprime(p=3,9999,ispseudoprime(t=eval(Str(p,t)))&print(t)) \\\\ - M. F. Hasler, Apr 05 2008

Extensions

More terms from Ray Chandler, Mar 28 2004

A092449 Composite numbers in A092447.

Original entry on oeis.org

753, 11753, 1311753, 19171311753, 2319171311753, 292319171311753, 31292319171311753, 3731292319171311753, 413731292319171311753, 43413731292319171311753, 4743413731292319171311753
Offset: 1

Views

Author

Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004

Keywords

Extensions

More terms from Ray Chandler, Mar 28 2004

A317903 a(n) = A038394(n)^^A038394(n) (mod 10^len(A038394(n))), where ^^ indicates tetration or hyper-4 (e.g., 3^^4=3^(3^(3^3))).

Original entry on oeis.org

4, 76, 176, 4176, 314176, 91314176, 891314176, 80891314176, 88080891314176, 5288080891314176, 705288080891314176, 10705288080891314176, 2410705288080891314176, 912410705288080891314176, 42912410705288080891314176, 9242912410705288080891314176, 989242912410705288080891314176
Offset: 1

Views

Author

Marco Ripà, Aug 10 2018

Keywords

Comments

For any n >= 2, a(n) (mod 10^len(A038394(n))) == a(n + 1) (mod 10^len(A038394(n))), where len(k) := number of digits in k. Assuming len(a(n))>1, this is a general property of every concatenated sequence with fixed rightmost digits (such as A014925 or A092447), as shown in Ripà's book "La strana coda della serie n^n^...^n".

Examples

			For n = 6, a(6) = 13117532^^13117532 (mod 10^8) == 91314176.
		

References

  • Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6

Crossrefs

Cf. A038394, A068670, A171882 (tetration), A317824.

Programs

  • PARI
    tmod(b, n) = {if (b % n == 0, return (0)); if (b % n == 1, return (1)); if (gcd(b, n)==1, return (lift(Mod(b, n)^tmod(b, lift(znorder(Mod(b, n))))))); lift(Mod(b, n)^(eulerphi(n) + tmod(b, eulerphi(n))));}
    f(n) = fromdigits(concat([digits(p) | p<-Vecrev(primes(n))])); \\ A038394
    a(n) = if (n==1, 4, my(x=f(n)); tmod(x, 10^#Str(x))); \\ Michel Marcus, Sep 12 2021

Formula

a(n) = (p(n)p(n-1)_p(n-2)...3_2)^^(p(n)_p(n-1)_p(n-2)...3_2) (mod 10^len(p(n)_p(n-1)_p(n-2)..._3_2)), where len(k) := number of digits in k.

Extensions

More terms from Jinyuan Wang, Aug 30 2020

A100003 Prime numbers p such that the concatenation of all odd primes up through p in decreasing order is prime.

Original entry on oeis.org

3, 5, 17, 89, 383, 8831
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

Comments

Next term is greater than 4400th prime and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, 4202.
We can see the prime corresponding to 383 (the 5th term of the sequence) in the page related to puzzle 8 of the website of Carlos Rivera.
a(7) > prime(28800) = 335033. - Giovanni Resta, Apr 01 2013

Examples

			17 is in the sequence because 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
		

Crossrefs

The actual prime concatenations in A092448 and the original concatenations in A092447. - Dmitry Kamenetsky, Mar 02 2009

Programs

  • Mathematica
    Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[Prime[n]]], {n, 2, 4413}]
    Prime[#]&/@Select[Range[100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Prime[Range[#,2,-1]]]]]&] (* To generate a(6) increase the Range by 1000, but the program will run a long time. *) (* Harvey P. Dale, Nov 27 2015 *)

A086043 Concatenation of first n twin primes.

Original entry on oeis.org

3, 35, 357, 35711, 3571113, 357111317, 35711131719, 3571113171929, 357111317192931, 35711131719293141, 3571113171929314143, 357111317192931414359, 35711131719293141435961, 3571113171929314143596171, 357111317192931414359617173, 357111317192931414359617173101
Offset: 1

Views

Author

Cino Hilliard, Sep 08 2003

Keywords

Comments

After 3, 357111317192931414359 is the only prime in the sequence for n up to 10000.
Although 5 appears in two twin prime pairs (3, 5) and (5, 7), 5 is concatenated only once in the sequence. - Daniel Forgues, Aug 23 2016
a(n) == 0 mod 3 for n odd, a(n) == 2 mod 3 for n even. - Robert Israel, Sep 01 2016

Crossrefs

Programs

  • Maple
    Primes:= select(isprime, {seq(i,i=1..100,2)}):
    T1:= Primes intersect map(`+`,Primes,2):
    Twins:= sort(convert(T1 union map(`-`,T1,2),list)):
    dcat:= (a,b) -> a*10^(1+ilog10(b))+b:
    A[1]:= 3:
    for n from 2 to nops(Twins) do A[n]:= dcat(A[n-1],Twins[n]) od:
    seq(A[i],i=1..nops(Twins)); # Robert Israel, Sep 01 2016
  • Mathematica
    Table[FromDigits@ Flatten@ Map[IntegerDigits, Take[#, n]], {n, Length@ #}] &[Union@ Join[#, # + 2] &@ Select[Prime@ Range@ 17, NextPrime@ # - 2 == # &]] (* Michael De Vlieger, Sep 01 2016 *)
    Module[{tps=Union[Flatten[Select[Partition[Prime[Range[50]],2,1],#[[2]]-#[[1]] == 2&]]]},FromDigits[Flatten[IntegerDigits/@#]]&/@Table[Take[tps,n],{n,Length[tps]}]] (* Harvey P. Dale, Jun 16 2022 *)
  • PARI
    concattwprb(n) = { y=3; forprime(x=5,n, if(isprime(x+2) || isprime(x-2), y=eval(concat(Str(y),Str(x))); print1(y",") ) ) }

Extensions

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar
Showing 1-5 of 5 results.