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A178701 An irregular array read by rows. The k-th entry of row r is the number of r-digit primes with digit sum k. 3
1, 0, 1, 1, 0, 1, 2, 2, 2, 3, 3, 3, 1, 1, 2, 1, 1, 2, 4, 7, 7, 12, 13, 16, 16, 13, 18, 12, 11, 6, 4, 1, 0, 0, 4, 8, 20, 19, 31, 52, 67, 77, 93, 101, 116, 95, 92, 91, 63, 51, 29, 30, 16, 5, 0, 1, 0, 4, 12, 28, 45, 95, 143, 236, 272, 411, 479, 630, 664, 742, 757, 741, 706, 580, 528, 379, 341, 205, 166, 84, 62, 34, 13, 4, 2, 0, 2, 14, 58, 76, 204, 389, 660, 852, 1448, 1971, 2832, 3101, 4064, 4651, 5393, 5376, 5570, 5785, 5287, 4796 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Each row, r, has 6r-1 terms. The first row does not account for the prime 3 and its count of 1.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..320

Craig Mayhew, Sums of digits of primes

EXAMPLE

To begin the second row, only 11 has digit-sum 2, so the first term is 1; both 13 & 31 have digit-sum 4 so the second term is 2; both 23 & 41 have digit-sum 5, so the third term is 2; etc.

To begin the third row, only 101 -> 2, so its first term is 1, both 103 & 211 -> 4 so its second term is 2; 113, 131, 311 & 401 ->5, so its third term is 4; etc.

\k .2,..4,..5,...7,...8,...10,...11,....13,....14,....16,.....17,.....19,.....20,.....22,......23,......25,......26,...,

r\

.1: 1,..0,..1,...1,...0}

.2: 1,..2,..2,...2,...3,....3,....3,.....1,.....1,.....2,......1}

.3: 1,..2,..4,...7,...7,...12,...13,....16,....16,....13,.....18,.....12,.....11,......6,.......4,.......1,.......0}

.4: 0,..4,..8,..20,..19,...31,...52,....67,....77,....93,....101,....116,.....95,.....92,......91,......63,......51, ...,

.5: 0,..4,.12,..28,..45,...95,..143,...236,...272,...411,....479,....630,....664,....742,.....757,.....741,.....706, ...,

.6: 0,..2,.14,..58,..76,..204,..389,...660,...852,..1448,...1971,...2832,...3101,...4064,....4651,....5393,....5376, ...,

.7: 0,..5,.21,..95,.138,..420,..773,..1747,..2329,..4616,...6456,..10496,..12743,..18710,...22447,...29209,...32075, ...,

.8: 0,..4,.24,.154,.212,..787,.1705,..4214,..5721,.12546,..19040,..34639,..43707,..71879,...92223,..135728,..155461, ...,

.9: 0,..2,.26,.226,.372,.1457,.3312,..9159,.13320,.32077,..50752,.102027,.138554,.249053,..331920,..535444,..655423, ...,

10: 0,.11,.42,.278,.547,.2395,.6090,.19204,.27894,.75517,.128909,.284482,.391199,.772365,.1087932,.1919618,.2427462, ...,

etc.

MATHEMATICA

dir[n_] := Floor[(3 n + 2)/2]; inv[n_] := Floor[(2 n - 1)/3]; f[n_] := Block[{p = NextPrime[10^(n - 1)], t = Table[0, {inv[9 n]}]}, While[p < 10^n, t[[ inv[Plus @@ IntegerDigits@ p]]]++; p = NextPrime@ p]; t]; Array[f, 5] // Flatten

CROSSREFS

Cf. A000040, A006880, A007605, A177868, A178183, A178447, A178571, A178605, A178876, A178879, A178884.

Row sums (except for the first term) give A006879. The indices k are given by A001651 (beginning with 2).

Sequence in context: A322062 A071451 A177868 * A117501 A181611 A064740

Adjacent sequences:  A178698 A178699 A178700 * A178702 A178703 A178704

KEYWORD

nonn,tabf

AUTHOR

Robert G. Wilson v, Dec 29 2010

STATUS

approved

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Last modified March 24 19:42 EDT 2019. Contains 321448 sequences. (Running on oeis4.)