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A136118
Least index m>0 such that A136117(n)-A000326(m) is again a pentagonal number.
11
5, 4, 7, 12, 19, 17, 25, 20, 10, 28, 45, 42, 39, 17, 37, 21, 36, 35, 13, 33, 65, 28, 67, 32, 52, 40, 74, 31, 70, 85, 35, 16, 60, 70, 77, 68, 42, 30, 105, 76, 59, 26, 74, 49, 115, 19, 125, 115, 102, 110, 92, 56, 103, 29, 145, 100, 114, 77, 92, 47, 63, 108, 152, 95, 22, 116
OFFSET
1,1
EXAMPLE
a(1)=5 is the least integer m>0 such that A136117(1)-P(m) is a pentagonal number, namely P(7)-P(5)=70-35=35=P(5).
a(2)=4 is the least integer m>0 such that A136117(2)-P(m) is a pentagonal number, namely P(8)-P(4)=92-22=70=P(7).
PROG
(PARI) A136118vect(n, i=-1)=vector(n, k, until(0, for(j=2, #n=sum2sqr((i+=6)^2+1), n[j]%6==[5, 5]||next; n=n[j]; break(2))); n[1]\6+1) /* This uses sum2sqr(), cf. A133388. Below some simpler but much slower code. */
my(P=A000326(n)=n*(3*n-1)/2, isPent(t)=P(sqrtint(t*2\3)+1)==t); for(i=1, 299, for(j=1, (i+1)\sqrt(2), isPent(P(i)-P(j))&print1(j", ")||next(2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Dec 25 2007
STATUS
approved