A229157
Primes of the form T(n) + C(n) - 1 where T(n) and C(n) are n-th triangular and cube numbers.
Original entry on oeis.org
73, 139, 547, 773, 2287, 4231, 8209, 9491, 36497, 111767, 118873, 177211, 217829, 316777, 391717, 596273, 889391, 1005049, 1035451, 1163189, 1265597, 1301023, 1449337, 1735259, 2105407, 2524771, 3319123, 4755827, 5467351, 6246523, 6348829, 6662437, 8636239, 9151273
Offset: 1
a(3)=547: T(8)+C(8)-1 = (1/2)*8*(8+1)+8^3-1 = 547 which is prime.
a(4)=773: T(9)+C(9)-1 = (1/2)*9*(9+1)+9^3-1 = 773 which is prime.
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KD:= proc() local a,b,d; a:= (1/2)*n*(n+1);b:=n^3; d:=a+b-1; if isprime(d) then RETURN(d): fi;end:seq(KD(),n=1..500);
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.
Original entry on oeis.org
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
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.
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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);
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select(isprime, vector(100,n,n^3+3/2*n^2+n/2+1)) \\ Charles R Greathouse IV, Sep 15 2013
A229960
Primes of the form n^3 - T(n) - 1 where T(n) is the n-th triangular number.
Original entry on oeis.org
53, 109, 683, 4759, 7789, 9029, 13523, 15299, 45989, 63179, 68059, 90089, 116423, 174019, 225089, 370619, 610469, 700963, 994949, 1025149, 1119403, 1398599, 1594709, 1898873, 2291189, 2561899, 2734129, 2975543, 3038039, 3296773, 3784169, 3857489, 5913269, 6212483
Offset: 1
a(2) = 109 since 5^3 - T(5) - 1 = 125 - 15 - 1 = 109, which is prime.
a(6) = 9029 since 21^3 - T(21) - 1 = 9261 - 231 - 1 = 9029 which is prime.
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KD:= proc() local a,b,d; a:= n^3;b:=(1/2)*n*(n+1); d:=a-b-1; if isprime(d) then RETURN(d): fi;end: seq(KD(),n=1..500);
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Select[Table[(n^3) - (n/2*(n + 1)) - 1, {n, 200}], PrimeQ]
Showing 1-3 of 3 results.
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