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A090190 Symmetric primes: an odd prime p is symmetric if there exists an odd prime q such that |p-q| = gcd(p-1,q-1). 4
3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 269, 271, 277, 281, 283, 293, 307, 311 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n=1..10000

William Banks, Paul Pollack and Carl Pomerance, Symmetric primes revisited, arXiv:1908.06161 [math.NT], 2019.

Rob Burns, Extremely symmetric primes, arXiv:2005.02922 [math.NT], 2020.

P. Fletcher, W. Lindgren and C. Pomerance, Symmetric and asymmetric primes, J. Number Theory 58 (1996) 89-99.

EXAMPLE

Any twin prime is symmetric since 2=gcd(p-1,p+1) for any odd prime p.

MATHEMATICA

f[n_] := Block[{k = 2}, While[k < 10^3 && Abs[n - Prime[k]] != GCD[n - 1, Prime[k] - 1], k++ ]; If[k == 10^3, 0, Prime[k]]]; Select[ Prime[ Range[2, 100]], f[ # ] != 0 &] (* Robert G. Wilson v, Sep 19 2004 *)

CROSSREFS

Complement gives A090191.

Sequence in context: A065389 A123567 A059645 * A325143 A276357 A065041

Adjacent sequences:  A090187 A090188 A090189 * A090191 A090192 A090193

KEYWORD

nonn

AUTHOR

Steven Finch, Jan 21 2004

EXTENSIONS

More terms from Robert G. Wilson v, Sep 19 2004

STATUS

approved

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)