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URL: https://oeis.org/A217199

⇱ A217199 - OEIS

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A217199
Odd primes p such that 2p-1 is prime and no p is equal to 2q-1 with q in the sequence.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Sep 27 2012
STATUS
approved