The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A298730

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A298730

Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^(k*(k+1)/2).
(history; published version)

#26 by Susanna Cuyler at Fri Mar 09 21:15:27 EST 2018

STATUS

proposed

approved

#25 by Ilya Gutkovskiy at Fri Mar 09 13:42:27 EST 2018

STATUS

editing

proposed

#24 by Ilya Gutkovskiy at Fri Mar 09 13:34:45 EST 2018

CROSSREFS

Cf. A000217, A000294, A007294, A291655, A298850.

#23 by Ilya Gutkovskiy at Fri Mar 09 13:30:32 EST 2018

NAME

allocated for Ilya Gutkovskiy

Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^(k*(k+1)/2).

DATA

1, 1, 1, 4, 4, 4, 16, 16, 16, 44, 54, 54, 126, 156, 156, 315, 435, 435, 780, 1060, 1115, 1856, 2576, 2741, 4214, 5804, 6464, 9446, 12924, 14464, 20324, 27818, 31778, 43166, 58232, 66977, 89396, 120000, 139255, 181274, 240405, 282000, 362457, 476334, 560709, 708893, 924923, 1096773, 1372597

OFFSET

0,4

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^A000217(k))^A000217(k).

MATHEMATICA

nmax = 48; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)/2))^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000217, A000294, A007294, A291655.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Mar 09 2018

STATUS

approved

editing

#22 by Ilya Gutkovskiy at Fri Mar 09 13:30:32 EST 2018

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#21 by Michel Marcus at Fri Mar 09 10:25:35 EST 2018

STATUS

reviewed

approved

#20 by Joerg Arndt at Fri Mar 09 09:50:53 EST 2018

STATUS

proposed

reviewed

#19 by Bruno Berselli at Fri Mar 09 08:36:55 EST 2018

STATUS

editing

proposed

#18 by Bruno Berselli at Fri Mar 09 08:36:51 EST 2018

NAME

Prime numbers whose digits begin with 777.

DATA

77711, 77713, 77719, 77723, 77731, 77743, 77747, 77761, 77773, 77783, 77797, 777001, 777011, 777013, 777031, 777041, 777071, 777097, 777103, 777109, 777137, 777143, 777151, 777167, 777169, 777173, 777181, 777187, 777191, 777199, 777209, 777221, 777241, 777247, 777251, 777269, 777277, 777313

OFFSET

1,1

MATHEMATICA

With[{w = ConstantArray[7, 3]}, Select[Map[FromDigits[Join @@ {w, #}] &, IntegerDigits@ Range[320]], PrimeQ]] (* Michael De Vlieger, Jan 28 2018 *)

CROSSREFS

Cf. A167282, A298729.

KEYWORD

base,nonn,changed

recycled

AUTHOR

Yohei Furutono, Jan 25 2018

STATUS

proposed

editing

#17 by Bruno Berselli at Thu Mar 08 03:17:12 EST 2018

STATUS

editing

proposed

Discussion

Thu Mar 08

03:44

Joerg Arndt: I am on the side of rejection, but like to leave the decision to the other editors.