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A224934 Primes p for which there exists no prime q, different from p, such that p+q-1 is the next prime after p. 1
2, 3, 89, 113, 293, 317, 359, 389, 401, 449, 479, 491, 683, 701, 719, 743, 761, 773, 839, 863, 887, 911, 929, 953, 983, 1109, 1163, 1193, 1327, 1373, 1409, 1439, 1523, 1559, 1571, 1583, 1637, 1669, 1733, 1823, 1847, 1979, 2003, 2039, 2153, 2179, 2213, 2243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If we relax the restriction on q, where q is different from p, 2 and 3 fail to be members of this sequence.

Primes p = prime(k) for which A076368(k+1) = p or A076368(k+1) is composite. - Robert Israel, Nov 21 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

89 is in the list because there exists no prime q such that 89 + q - 1 = 97.

MAPLE

N:= 10^4: # to get all terms p for which the next prime <= N

P:= select(isprime, [2, seq(i, i=3..N, 2)]):

G:= P[2..-1]-P[1..-2]:

P[select(t -> G[t]=P[t]-1 or not isprime(G[t]+1), [$1..nops(G)])]; # Robert Israel, Nov 21 2016

MATHEMATICA

t = {}; Do[p = Prime[n]; If[FreeQ[Table[k = p + Prime[i] - 1, {i, n - 1}], Prime[n + 1]], AppendTo[t, p]], {n, 335}]; t

CROSSREFS

Cf. A076368, A224748.

Sequence in context: A041401 A103013 A246121 * A299691 A042901 A002983

Adjacent sequences:  A224931 A224932 A224933 * A224935 A224936 A224937

KEYWORD

nonn

AUTHOR

Jayanta Basu, Apr 20 2013

STATUS

approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)