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A237183 Primes p with phi(p+1) - 1 and phi(p+1) + 1 both prime, where phi(.) is Euler's totient function. 2
7, 11, 13, 17, 37, 41, 53, 61, 97, 151, 181, 197, 227, 233, 251, 269, 277, 397, 433, 457, 487, 541, 557, 571, 593, 619, 631, 719, 743, 769, 839, 857, 929, 941, 947, 953, 1013, 1021, 1049, 1061, 1063, 1201, 1237, 1277, 1307, 1321, 1367, 1481, 1511, 1549 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to part (i) of the conjecture in A237168, this sequence should have infinitely many terms.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 7 since 7, phi(7+1) - 1 = 3 and phi(7+1) + 1 = 5 are all prime, but phi(2+1) - 1 = phi(3+1) - 1 = phi(5+1) - 1 = 1 is not prime.

MATHEMATICA

PQ[n_]:=PrimeQ[EulerPhi[n]-1]&&PrimeQ[EulerPhi[n]+1]

n=0; Do[If[PQ[Prime[k]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10000}]

Select[Prime[Range[300]], And@@PrimeQ[EulerPhi[#+1]+{1, -1}]&] (* Harvey P. Dale, Mar 06 2014 *)

PROG

(PARI) s=[]; forprime(p=2, 2000, if(isprime(eulerphi(p+1)-1) && isprime(eulerphi(p+1)+1), s=concat(s, p))); s \\ Colin Barker, Feb 04 2014

CROSSREFS

Cf. A000010, A000040, A001359, A006512, A072281, A237127, A237130, A237168.

Sequence in context: A038877 A019351 A032666 * A153321 A060772 A257125

Adjacent sequences:  A237180 A237181 A237182 * A237184 A237185 A237186

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Feb 04 2014

STATUS

approved

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Last modified May 21 09:30 EDT 2022. Contains 353908 sequences. (Running on oeis4.)