A217199 Odd primes p such that 2p-1 is prime and no p is equal to 2q-1 with q in the sequence.

3, 7, 19, 31, 79, 97, 139, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 691, 727, 811, 829, 937, 967, 1009, 1069, 1171, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1759, 1867, 2011, 2029, 2089, 2131, 2179, 2221, 2281

Offset

1,1

Comments

At each step, the smallest possible p is chosen.

These are the primes described in lemma 2 of the paper by Holt. - T. D. Noe, Sep 28 2012

This sequence was used by Holt (2003) to prove that there are at least two solutions k to phi(n+k) = phi(k) for all even n <= 1.38*10^26595411. - Amiram Eldar, Mar 19 2021

Links

Michel Marcus, Table of n, a(n) for n = 1..1000

Jeffery J. Holt, The minimal number of solutions to phi(n)=phi(n+k), Math. Comp., 72 (2003), 2059-2061.

A. Schinzel and Andrzej Wakulicz, Sur l'équation phi(x+k)=phi(x), I., Acta Arith. 4 (1958), 181-184.

Mathematica

t = {}; p = 2; Do[p = NextPrime[p]; If[PrimeQ[2*p - 1] && ! MemberQ[2*t - 1, p], AppendTo[t, p]], {PrimePi[2281]}]; t

Prog

(PARI) intab(val, tab) = {for (ii=1, length(tab), if (tab[ii] == val, return (1); ); ); return(0); }
lista(nn) = {tab = []; for (i=1, nn, len = length(tab); if (len == 0, p = 3, p = nextprime(tab[len]+1)); while (! isprime(2*p-1) || intab((p+1)/2, tab) , p = nextprime(p+1); ); tab = concat(tab, p); print1(p, ", "); ); }

Crossrefs

Cf. A007015, A110581, A217198, A342701.

Sequence in context: A093932 A141173 A145472 * A077313 A102271 A145039

Adjacent sequences: A217196 A217197 A217198 * A217200 A217201 A217202

Keyword

nonn

Author

Michel Marcus, Sep 27 2012

Status

approved