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A136118

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

#4 by M. F. Hasler at Fri May 29 06:29:36 EDT 2015

STATUS

editing

approved

#3 by M. F. Hasler at Thu May 14 18:38:42 EDT 2015

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).

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: */ P(n)=n*(3*n-1)/2 /* a.k.a. A000326 */ /*****newline*****/ isPent(t)=P(sqrtint(t*2\3)+1)==t /*****newline*****/ for(i=1, 299, for(j=1, (i+1)\sqrt(2), isPent(P(i)-P(j))&print1(j", ")|next(2)))

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)))

STATUS

approved

editing

Discussion

Fri May 29

04:45

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A136118 and click the button that reads
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  - The OEIS Server

06:29

M. F. Hasler: (only formatting : line breaks removed / added)

#2 by Russ Cox at Sat Mar 31 13:48:25 EDT 2012

AUTHOR

_M. F. Hasler (Maximilian.Hasler(AT)gmail.com), _, Dec 25 2007

Discussion

Sat Mar 31

13:48

OEIS Server: https://oeis.org/edit/global/893

#1 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

NAME

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

DATA

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: */ P(n)=n*(3*n-1)/2 /* a.k.a. A000326 */ /*****newline*****/ isPent(t)=P(sqrtint(t*2\3)+1)==t /*****newline*****/ 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.

KEYWORD

nonn

AUTHOR

M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 25 2007

STATUS

approved