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a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 7's.
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11
8, 108, 878, 870, 8813, 27924, 84129, 882483, 2788865, 7601169, 88190572, 421518419, 4204014483, 26034169427, 42305694389, 88022598108, 546605779129, 2788866736108, 69048807207508, 98844816642745, 88187696578, 2516, 5270458024477168, 26772616052167516, 166654612230648203, 521323093463907254
EXAMPLE
From Jesse Sealand, Oct 05 2019: (Start)
a(2) = 108 since A002378(36) = 11772; a(3) = 878 since A002378(182) = 771762; a(4) = 870 since A002378(1817) = 757770, etc. (End).
PROG
(Python)
k, m = 1, 2
while True:
if str(m).count('7') == n:
return k
k += 1
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 0's.
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10
0, 24, 100, 624, 1000, 10001, 10000, 100001, 100000, 1000001, 1000000, 10000001, 10000000, 100000001, 100000000, 1000000001, 1000000000, 10000000001, 10000000000
EXAMPLE
a(3) = 100 since A002378(100) = 10100; a(4) = 624 since A002378(624) = 390000, etc. (End).
MATHEMATICA
a[n_] := Block[{a = 0}, While[Count[IntegerDigits[a*(a + 1)], 0] != n, ++a]; Return[a]]; a /@ Range[1, 10] (* Julien Kluge, Dec 15 2016 *)
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 1's.
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10
3, 10, 105, 1010, 10203, 33928, 105551, 335128, 1054130, 12313046, 100573943, 333192303, 1054092885, 4261585525, 30184681729, 133083117303, 331829837885, 4136557897710, 11666683809854, 105410706823885, 333183899837885, 3333333637837885, 6466156610468989, 33928029520312720, 138242940872632303
EXAMPLE
a(3) = 105 since A002378(105) = 11130; a(4) = 1010 since A002378(1010) = 1021110, etc. (End).
Smallest oblong (promic) number containing exactly n 2's.
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10
2, 272, 20022, 210222, 2127222, 112222242, 1329222222, 222721228422, 222222202620, 12225222042222, 222922622262242, 22222622629269222, 222262242222052122, 22222222222226402, 222222624222746822222, 13222522222222257222852, 222222225263222925292272
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 3's.
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10
5, 36, 182, 1817, 4830, 5773, 153079, 577355, 3659694, 18366636, 182574188, 576484036, 1839384036, 17701331569, 36542213005, 485935528988, 1814754484036, 5755287250288, 5773506159694, 182738579159694, 230940107675430, 1820173984357898, 18202838331788627, 57475066797119386, 182305878493709942
EXAMPLE
a(2) = 36 since A002378(36) = 1332; a(3) = 182 since A002378(182) = 33306; a(4) = 1817 since A002378(1817) = 3303306, etc. (End)
MATHEMATICA
With[{s = 2 Accumulate[Range[0, 10^6]]}, Table[-1 + FirstPosition[s, _?(DigitCount[#, 10, 3] == n &)][[1]], {n, 8}]] (* Michael De Vlieger, Oct 05 2019 *)
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 4's.
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10
6, 66, 215, 681, 6681, 12018, 201115, 1531159, 6541784, 21058215, 156340764, 675098840, 5868938806, 6666461193, 120186956049, 586862372693, 1115546688777, 4176295540840, 66589372231193, 66634408865198, 210842150539318, 2108185118566309, 21011769217380159, 185591342591574215, 67412496945629038
EXAMPLE
a(2) = 66 since A002378(66) = 4422; a(3) = 215 since A002378(215) = 46440; a(4) = 681 since A002378(681) = 464442, etc. (End).
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 5's.
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10
7, 23, 74, 2248, 2292, 23506, 50552, 742667, 2357022, 22706949, 74555050, 703955648, 745020507, 3996943276, 74333434976, 244040827632, 505525029504, 5963015642907, 23548897033949, 156701172827632, 745354652534976, 758666893673274, 7453694087868501, 77198164845775648, 505525028614365003
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 6's.
+10
10
2, 60, 257, 816, 4082, 77887, 258237, 816512, 4546060, 25820081, 103276578, 815209584, 816472087, 2581876578, 24834787435, 258140787487, 1239623599592, 7978512779247, 78515384904912, 121105886176546, 816494743559742, 6608227190863421, 8164653370882732, 81281404248860431, 81649676463937177
EXAMPLE
a(2) = 60 since A002378(60) = 3660; a(3) = 257 since A002378(257) = 66306; a(4) = 816 since A002378(816) = 666672, etc. (End).
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 8's.
+10
10
13, 113, 886, 2861, 9213, 93855, 298053, 1359738, 2967970, 26189480, 220183761, 433461519, 3462498821, 28962801813, 43462498821, 722411301260, 942809540088, 9049247973113, 29354537778480, 195230348268113, 1970200215432144, 2426703296418144, 2233582298883761, 93802389568778480, 242669917148548480
EXAMPLE
a(2) = 113 since A002378(113) = 12882; a(3) = 886 since A002378(886) = 785882; a(4) = 2861 since A002378(2861) = 8188182, etc. (End).
a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 9's.
+10
10
9, 31, 890, 2234, 14131, 30331, 173031, 969520, 9958890, 31617890, 360542549, 547631234, 3316547890, 17318486343, 114017542334, 356363452109, 3065925634968, 9995498986343, 44045425415132, 173193446755643, 1414213562370264, 4471015432706534, 31575306806579083, 171463720944111031, 141138230008594765
EXAMPLE
a(3) = 890 since A002378(890) = 792990; a(4) = 2234 since A002378(2234) = 4992990, etc. (End).
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