The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A245625 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A245625

Sequence of distinct least nonnegative numbers such that the average of the first n terms is a square.
(history; published version)

#14 by N. J. A. Sloane at Fri Nov 07 00:11:41 EST 2014

STATUS

proposed

approved

#13 by Derek Orr at Wed Nov 05 13:00:40 EST 2014

STATUS

editing

proposed

Discussion

Wed Nov 05

13:12

Michel Marcus: yes it seems there is a hiccup there 
because afterwards it appears every other term is also a square

13:14

Derek Orr: Similar to the sequences of the triangular numbers. But perhaps it always hiccups after a certain n

#12 by Derek Orr at Wed Nov 05 13:00:27 EST 2014

FORMULA

a(2*n+1) = n^2.

a(2*n) = 5*n^2 - 4*n + 1.

STATUS

reviewed

editing

Discussion

Wed Nov 05

13:00

Derek Orr: Thanks, I retracted them

#11 by Colin Barker at Wed Nov 05 12:24:02 EST 2014

STATUS

proposed

reviewed

#10 by Derek Orr at Wed Nov 05 10:33:20 EST 2014

STATUS

editing

proposed

Discussion

Wed Nov 05

12:24

Colin Barker: Derek, the sequence seems to go astray following the term  256, as the next but one term should be, according to your formulae, 289, but it is 1514. Or perhaps the formulae are incorrect as I see that you don't use them in your PARI code.

#9 by Derek Orr at Wed Nov 05 10:33:16 EST 2014

NAME

allocated for Derek OrrSequence of distinct least nonnegative numbers such that the average of the first n terms is a square.

DATA

0, 2, 1, 13, 4, 34, 9, 65, 16, 106, 25, 157, 36, 218, 49, 289, 64, 370, 81, 461, 100, 562, 121, 673, 144, 794, 169, 925, 196, 1066, 225, 1217, 256, 1378, 1514, 324, 1693, 361, 1882, 400, 2081, 441, 2290, 484, 2509, 529, 2738, 576, 2977, 625, 3226, 676, 3485, 729, 3754, 784, 4033, 841

OFFSET

1,2

FORMULA

a(2*n+1) = n^2.

a(2*n) = 5*n^2 - 4*n + 1.

PROG

(PARI) v=[]; n=0; while(n<10^4, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=0, n, if(i^2>(num/(#v+1)), break); if(i^2==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=0; break))); n++)

CROSSREFS

Cf. A085047.

KEYWORD

allocated

nonn

AUTHOR

Derek Orr, Nov 05 2014

STATUS

approved

editing

#8 by Derek Orr at Wed Nov 05 10:33:16 EST 2014

NAME

allocated for Derek Orr

KEYWORD

recycled

allocated

#7 by Alois P. Heinz at Tue Nov 04 18:26:49 EST 2014

STATUS

editing

approved

#6 by Alois P. Heinz at Tue Nov 04 18:21:08 EST 2014

NAME

Rene Peer

DATA

3, 4, 5, 7, 9, 10, 11, 14, 15, 44, 53, 55, 84, 91, 115, 137, 142, 203, 255, 261, 275, 283, 285, 293, 307, 319, 324, 459

OFFSET

1,1

COMMENTS

For every a in the list p(a) is prime

FORMULA

a(n)=log(p-1155;2)

p(a)=1155+2^a

EXAMPLE

For a=3 the p(3)=1155+2^3=1163 solution is prime

PROG

Pari: {while(n<500, a=n-1; p=1155+2^a; if(isprime(p), print(a)); n=n+1)}

KEYWORD

nonn,changed

recycled

AUTHOR

Rene Peer, Jul 27 2014

STATUS

proposed

editing

#5 by Joerg Arndt at Tue Nov 04 12:39:29 EST 2014

STATUS

editing

proposed