

A090120


Numbers x such that nextprime(x^2)  prevprime(x^2) = 4.


1



3, 4, 9, 10, 14, 15, 20, 21, 26, 33, 40, 110, 117, 124, 146, 206, 237, 250, 273, 303, 309, 326, 340, 350, 387, 429, 436, 440, 441, 447, 470, 513, 561, 573, 609, 634, 686, 704, 807, 897, 920, 1004, 1035, 1054, 1060, 1071, 1113, 1124, 1143, 1156, 1233, 1239
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OFFSET

1,1


COMMENTS

Note that the gap=4 is partitioned either as 2+2 or as 3+1; 1+3 never occurs since n^21 is composite if n>2.


LINKS

Table of n, a(n) for n=1..52.


FORMULA

Solutions to {x; A007918(x^2)A007917(x^2) = 4}.


EXAMPLE

n=3, n^2=9 is surrounded by closest primes: {7,[9],11};
n=10, n^2=100 is surrounded by {97,[100],101};


MATHEMATICA

Select[Range[3, 1500], NextPrime[#^2] == NextPrime[#^2, 1] + 4 &] (* Giovanni Resta, May 26 2018 *)


PROG

(PARI) isok(n) = nextprime(n^2)  precprime(n^2) == 4; \\ Michel Marcus, May 26 2018


CROSSREFS

Cf. A090116, A090117, A090118, A090119, A007917, A007918, A000720, A000040, A053001, A007491, A000290.
Sequence in context: A059985 A137709 A275538 * A129783 A301919 A093513
Adjacent sequences: A090117 A090118 A090119 * A090121 A090122 A090123


KEYWORD

nonn


AUTHOR

Labos Elemer, Jan 09 2004


STATUS

approved



