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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
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^2-1 is composite if n>2.
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 09 2004
STATUS
approved