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A090119 a(n)=nextprime[A090116(n)], the smallest prime following squares listed in A090116 and also the distance of a(n) from the preceding prime is 2n. 4
5, 11, 29, 367, 149, 631, 127, 1949, 541, 907, 3251, 1693, 2503, 10427, 5779, 10831, 10007, 22229, 30631, 25301, 121123, 76207, 93047, 157627, 212557, 35729, 119027, 1121509, 190979, 672439, 693943, 1004027, 259099, 1646101, 675713, 1207841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n) = nextprime[A090116(n)^2] = nextprime[A090117(n)] = p[1+pi[A090117(n)]] = A007918[A090116[n]].

EXAMPLE

n=7: a(7)=127 because 127-113=14=2.7 and 121=11 is between {127,113} closest primes to 121 a suitable square number. Also 127 is the smallest prime with this property.

MATHEMATICA

pre[x_ := Prime[PrimePi[x]] nex[x_ := Prime[PrimePi[x]+1] de[x_ := Prime[PrimePi[x]+1]-Prime[PrimePi[x]] t=Table[de[w^2], {w, 1, 50000}]; mt=Table[Min[Flatten[Position[t, 2*j]]], {j, 1, 100}] Table[nex[Part[mt, j]^2], {j, 1, Length[mt]}]

CROSSREFS

Cf. A090116-A090118, A007917, A007918, A000720, A000040, A053001, A007491, A000290.

Sequence in context: A001632 A234511 A053185 * A174922 A088484 A179256

Adjacent sequences:  A090116 A090117 A090118 * A090120 A090121 A090122

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 09 2004

STATUS

approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)