The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083809

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A083809

Let f(n) be the smallest prime == 1 mod n (cf. A034694). Sequence gives triangle T(j,k) = f^k(j) for 1 <= k <= j, read by rows.
(history; published version)

#21 by Charles R Greathouse IV at Thu Sep 08 08:45:10 EDT 2022

PROG

(MAGMAMagma) f:=function(n) m:=1; while not IsPrime(m*n+1) do m+:=1; end while; return m*n+1; end function; &cat[ [ k eq 1 select f(j) else f(Self(k-1)): k in [1..j] ]: j in [1..9] ]; // Klaus Brockhaus, May 30 2009

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#20 by Alois P. Heinz at Sat Mar 14 17:36:12 EDT 2015

STATUS

proposed

approved

#19 by Jon E. Schoenfield at Sat Mar 14 16:23:26 EDT 2015

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Sat Mar 14 16:23:21 EDT 2015

COMMENTS

It has been proved in the reference that for every prime p there exists a prime of the form k*p+1. Conjecture: sequence is infinite, i.e. , for every n there exists a prime of the form n*k+1 (cf. A034693).

REFERENCES

Amarnath Murthy, On the divisors of Smarandache Unary Sequence. Smarandache Notions Journal, Vol. 11, 2000.

MATHEMATICA

(* From J.F._Jean-François Alcover, _, May 31 2011, improved by _Robert G. Wilson v_ *)

PROG

(MAGMA) f:=function(n) m:=1; while not IsPrime(m*n+1) do m+:=1; end while; return m*n+1; end function; &cat[ [ k eq 1 select f(j) else f(Self(k-1)): k in [1..j] ]: j in [1..9] ]; [From _// _Klaus Brockhaus_, May 30 2009]

STATUS

approved

editing

#17 by N. J. A. Sloane at Thu Dec 05 19:56:15 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, May 08 2003

Discussion

Thu Dec 05

19:56

OEIS Server: https://oeis.org/edit/global/2075

#16 by Charles R Greathouse IV at Mon May 13 01:48:18 EDT 2013

COMMENTS

Both follow directly from Dirichlet's theorem. [_Charles R Greathouse IV, _, Feb 28 2012]

PROG

T(j, k)=for(i=1, k, j=f(j)); j \\ _Charles R Greathouse IV, _, Feb 28 2012

Discussion

Mon May 13

01:48

OEIS Server: https://oeis.org/edit/global/1914

#15 by Russ Cox at Fri Mar 30 17:27:40 EDT 2012

PROG

EXTENSIONS

Edited, corrected and extended by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, May 13 2003

Discussion

Fri Mar 30

17:27

OEIS Server: https://oeis.org/edit/global/145

#14 by Joerg Arndt at Wed Feb 29 05:27:33 EST 2012

STATUS

proposed

approved

#13 by Charles R Greathouse IV at Tue Feb 28 15:59:32 EST 2012

STATUS

editing

proposed

#12 by Charles R Greathouse IV at Tue Feb 28 15:58:53 EST 2012

COMMENTS

Both follow directly from Dirichlet's theorem. [Charles R Greathouse IV, Feb 28 2012]

LINKS

M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/">Smarandache Notions Journal</a>

Discussion

Tue Feb 28

15:59

Charles R Greathouse IV: Did Amarnath Murthy just conjecture Ditichlet's theorem?  Possibly the first comment should be removed (and mine modified).