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 A048975 Pairs of consecutive primes p, q, for which the smallest primitive root of q is 1 greater than the smallest primitive root of p. 1
 2, 3, 5, 7, 13, 17, 29, 31, 83, 89, 131, 137, 197, 199, 211, 223, 317, 331, 349, 353, 443, 449, 461, 463, 509, 521, 563, 569, 587, 593, 613, 617, 619, 631, 727, 733, 797, 809, 821, 823, 853, 857, 877, 881, 947, 953, 967, 971, 983, 991, 991, 997, 1061, 1063 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Paulo Ribenboim, The new book of prime number records, Springer, 1996, pp. 22-25. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Index entries for primes by primitive root EXAMPLE The primitive roots (mod 13) are 2, 6, 7, and 11, and the primitive roots (mod 17) are 3, 5, 6, 7, 10, 11, 12, and 14, so since 3 = 2 + 1, 13 and 17 are in the sequence. 991 is in the sequence twice because the smallest primitive roots for the three consecutive primes 983, 991, and 997 are 5, 6, and 7, respectively, so 991 appears as the larger of the pair (983,991) since 6 = 5 + 1, and as the smaller of the pair (991,997) since 7 = 6 + 1. MATHEMATICA Reap[ Do[ If[ PrimitiveRoot[p] + 1 == PrimitiveRoot[np = NextPrime[p]], Sow[p]; Sow[np]], {p, Prime /@ Range[200]}]][[2, 1]] (* Jean-François Alcover, Oct 04 2012 *) Flatten[{Prime[#], Prime[#+1]}&/@Flatten[Position[Partition[ PrimitiveRoot[ Prime[ Range[200]]], 2, 1], _?(#[[2]]-#[[1]]==1&), {1}, Heads->False]]] (* Harvey P. Dale, Dec 22 2014 *) PROG (PARI) forprime(p=2, 1061, if( lift(znprimroot(p)) + 1 == lift(znprimroot(nextprime(p+1))), print(p); print(nextprime(p+1)))) \\ Michael B. Porter, Mar 03 2013 CROSSREFS Sequence in context: A188809 A350443 A152449 * A009571 A087520 A117159 Adjacent sequences: A048972 A048973 A048974 * A048976 A048977 A048978 KEYWORD nice,nonn AUTHOR Felice Russo EXTENSIONS More terms from James A. Sellers, Apr 22 2000 STATUS approved

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Last modified June 23 12:51 EDT 2024. Contains 373648 sequences. (Running on oeis4.)