A136118 - OEIS

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A136118

Least index m>0 such that A136117(n)-A000326(m) is again a pentagonal number.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..66.

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

Cf. A000326, A136112-A136117.

Sequence in context: A245073 A021650 A141269 * A105665 A019129 A019208

Adjacent sequences: A136115 A136116 A136117 * A136119 A136120 A136121

KEYWORD

nonn

AUTHOR

M. F. Hasler, Dec 25 2007

STATUS

approved