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 A253108 Numbers n such that (sum of n^2 through (n+2)^2) + (n+1)^2 is prime. 1
 2, 4, 6, 9, 14, 17, 20, 21, 25, 32, 34, 35, 40, 45, 49, 51, 52, 56, 60, 62, 65, 76, 80, 82, 86, 87, 89, 94, 95, 96, 100, 104, 105, 107, 112, 114, 115, 116, 117, 124, 126, 135, 137, 140, 145, 147, 151, 164, 167, 172, 174, 179, 180, 181, 182, 199, 200, 202, 205, 206, 207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence is related to the Legendre conjecture. No terms == 3 mod 5 or == 1 mod 7 or 0 mod 11. - Robert Israel, Jun 24 2015 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE For n=2, n+1=3, n+2=4: we have Sum(n^2,(n+1)^2)=Sum(2^2,3^2)=Sum(4,9)=Sum(4+5+6+7+8+9)=39, Sum((n+1)^2,(n+2)^2)=Sum(3^2,4^2)=Sum(9,16)=Sum(9+10+11+12+13+14+15+16)=100, 39+100=139, 139 is prime; hence 2 is a term. MAPLE select(n -> isprime(4*n^3+14*n^2+20*n+11), [\$1..1000]); # Robert Israel, Dec 28 2014 MATHEMATICA Select[Range[250], PrimeQ[Total[Range[#^2, (#+2)^2]]+(#+1)^2]&] (* Harvey P. Dale, Aug 04 2022 *) PROG (PARI)for (n=1, 1000, if(isprime(4*n^3+14*n^2+20*n+11), print1(n", "))) CROSSREFS Sequence in context: A081225 A164140 A205883 * A198201 A281989 A328423 Adjacent sequences: A253105 A253106 A253107 * A253109 A253110 A253111 KEYWORD nonn AUTHOR César Aguilera, Dec 26 2014 EXTENSIONS a(47) corrected by Robert Israel, Jun 24 2015 STATUS approved

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Last modified December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)