

A119665


Sign in the term (2q +/ 1) for triangular numbers of the form q * (2q +/ 1) where both factors are primes (or prime powers).


0



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OFFSET

1


COMMENTS

As always, 1 is considered to be a prime power.


LINKS



EXAMPLE

a(1) = 1 since 1 = 1*1 and 1 = 2*1  1, a(2) = +1 since 3 = 1*3 and 3 = 2*1 + 1,
a(3) = 1 since 6 = 2*3 and 3 = 2*2  1, a(4) = +1 since 10 = 2*5 and 5 = 2*2 + 1,
a(5) = 1 since 15 = 3*5 and 5 = 2*3  1, a(6) = +1 since 21 = 3*7 and 7 = 2*3 + 1,
a(7) = 1 since 28 = 4*7 and 7 = 2*4  1, a(8) = +1 since 36 = 4*9 and 9 = 2*4 + 1,
a(9) = 1 since 45 = 5*9 and 9 = 2*5  1, a(10) = 1 since 55 = 5*11 and 11 = 2*5 + 1;
66 and 78 are the first triangular numbers not equal to a product of prime powers q*(2q+1);
a(11) = 1 since 91 = 7*13 and 13 = 2*7  1;
105 and 120 aren't of the required form, either;
a(12) = +1 since 136 = 8*17 and 17 = 2*8 + 1,
a(13) = 1 since 153 = 9*17 and 17 = 2*9  1,
a(14) = +1 since 171 = 9*19 and 19 = 2*9 + 1;
now 190, 210 and 231 aren't of the required form, which yields the first a(n) = a(n1):
a(15) = +1 since 253 = 11*23 and 23 = 2*11 + 1.  M. F. Hasler, Apr 21 2015


PROG

(PARI) for(q=1, 999, (isprimepower(q)q==1)&&forstep(j=1, 1, 2, (isprimepower(q*2+j)q*2+j==1)&&print1(j", "))) \\ M. F. Hasler, Apr 21 2015


CROSSREFS



KEYWORD

sign


AUTHOR



EXTENSIONS

Missing and wrong terms and offset corrected; more terms added by M. F. Hasler, Apr 21 2015


STATUS

approved



