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A248972 a(n) is the smallest b such that b^((p-1)/2) == -1 (mod p) where p = A080076(n) is the n-th Proth prime. 2
2, 2, 2, 3, 3, 5, 3, 5, 7, 3, 3, 3, 5, 3, 5, 7, 3, 5, 3, 3, 3, 5, 13, 3, 3, 3, 5, 3, 5, 7, 5, 13, 3, 3, 13, 3, 11, 5, 3, 3, 3, 11, 3, 11, 3, 3, 5, 3, 7, 3, 3, 5, 3, 5, 11, 3, 3, 5, 11, 3, 7, 5, 5, 3, 5, 3, 5, 3, 3, 3, 5, 3, 3, 3, 19, 3, 3, 3, 7, 7, 3, 3, 11, 5, 3, 3, 5, 3, 11, 5, 3, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Proth's theorem asserts that p=1+k*2^m (with odd k < 2^m) is prime if there exists b such that b^((p-1)/2) == -1 (mod n). This sequence lists the smallest b which certifies primality of A080076(n) via this relation.

For n > 3, a(n) is an odd prime. - Thomas Ordowski, Apr 23 2019

LINKS

Table of n, a(n) for n=1..92.

FORMULA

a(n) = A020649(A080076(n)) = A053760(k), where prime(k) = A080076(n). - Thomas Ordowski, Apr 23 2019

PROG

(PARI) A248972(n)=my(N=A080076[n]); for(a=0, 9e9, Mod(a, N)^(N\2)==-1&&return(a))

A080076=[]; forprime(p=1, 99999, isproth(p)&&(A080076=concat(A080076, p))&&print1(A248972(#A080076)", "))

isproth(x)={ !bittest(x--, 0) & (x>>valuation(x, 2))^2 < x }

CROSSREFS

Cf. A080076.

A subsequence of A020649 and of A053760.

Sequence in context: A237121 A329493 A139821 * A077563 A055256 A295630

Adjacent sequences:  A248969 A248970 A248971 * A248973 A248974 A248975

KEYWORD

nonn

AUTHOR

M. F. Hasler, Oct 18 2014

STATUS

approved

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Last modified August 14 08:08 EDT 2020. Contains 336480 sequences. (Running on oeis4.)