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URL: https://oeis.org/A228908

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A228908
Primes of the form T(n) + S(n) + C(n) + 1 where T(n), S(n) and C(n) are the n-th triangular, square and cube numbers.
2
43, 421, 613, 1951, 7411, 12973, 23143, 31249, 48619, 114073, 210631, 256033, 321403, 365509, 381061, 502441, 521641, 669901, 766039, 791431, 1015051, 1108693, 1242271, 1929751, 2121793, 2773471, 3759991, 3832999, 4057681, 5498329, 7133281, 7472011, 7587259
OFFSET
1,1
COMMENTS
Also primes of the form n^3 + 3/2*n^2 + 1/2*n + 1.
LINKS
EXAMPLE
a(3) = 613: T(8)+S(8)+C(8)+1 = 1/2*8*(8+1)+8^2+8^3+1 = 613 which is prime.
a(4) = 1951: T(12)+S(12)+C(12)+1 = 1/2*12*(12+1)+12^2+12^3+1 = 1951 which is prime.
MAPLE
KD:= proc() local a, b, c, d; a:= (1/2)*n*(n+1); b:=n^2; c:=n^3; d:=a+b+c+1; if isprime(d) then RETURN(d): fi; end:seq(KD(), n=1..500);
MATHEMATICA
With[{nn=300}, {tr=Accumulate[Range[nn]]}, {sq=Range[nn]^2}, {cu=Range[nn]^3}, Select[Table[tr[[n]]+sq[[n]]+cu[[n]]+1, {n, nn}], PrimeQ]] (* Harvey P. Dale, Dec 10 2025 *)
PROG
(PARI) select(isprime, vector(100, n, n^3+3/2*n^2+n/2+1)) \\ Charles R Greathouse IV, Sep 15 2013
CROSSREFS
Sequence in context: A142770 A142841 A142913 * A027002 A093673 A244769
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Sep 14 2013
STATUS
approved