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.

A029932 Primes with record values of the least positive prime primitive root.

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%I A029932 #30 Aug 04 2018 02:54:01
%S A029932 3,7,23,41,109,191,271,2791,11971,31771,190321,2080597,3545281,
%T A029932 4022911,73189117,137568061,443571241,565822531,1160260711,1622723341,
%U A029932 31552100581,81651092041,96736641541,1867622877121,5000346134911
%N A029932 Primes with record values of the least positive prime primitive root.
%C A029932 Other terms in the sequence: 39227234631271, 66597722601061 and 84054326426071 -Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008
%C A029932 Subsequence of A002230, considering only prime primitive roots. - _M. F. Hasler_, Jun 01 2018
%D A029932 R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
%D A029932 A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XLV.
%H A029932 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/p_roots.html">Counts of least primitive roots of prime numbers (Artin's conjecture)</a>
%H A029932 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/p_roots/t2.txt.gz">Least prime primitive roots</a>
%H A029932 A. Paszkiewicz and A. Schinzel, <a href="https://doi.org/10.1090/S0025-5718-02-01370-4">On the least prime primitive root modulo a prime</a>, Math. Comp. 71 (2002), no. 239, 1307-1321.
%H A029932 A. E. Western and J. C. P. Miller, <a href="/A002223/a002223.pdf">Tables of Indices and Primitive Roots</a>, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]
%H A029932 <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>
%t A029932 (* This program is not suitable for computing more than a dozen terms. *) max = 10^8; pprQ[r_, p_] := Union[Table[PowerMod[r, i, p], {i, 1, p+1}]] == coprimes; ppr[p_] := With[{spr = PrimitiveRoot[p]}, If[PrimeQ[spr], spr, coprimes = Select[Range[p-1], CoprimeQ[#, p]&]; For[r = NextPrime[ spr], True, r = NextPrime[r], If[pprQ[r, p], Return[r]]]]]; Reap[ For[ record=1; p=3, p<max, p = NextPrime[p], ppr1 = ppr[p]; If[ppr1 > record, record = ppr1; Print["p = ", p, " ppr = ", record]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Feb 25 2016 *)
%Y A029932 Cf. A060749, A002230, A084735.
%K A029932 nonn,nice
%O A029932 1,1
%A A029932 Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
%E A029932 Corrected by _Jud McCranie_, Jan 04 2001
%E A029932 2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008