A352511
Starts of runs of 4 consecutive Catalan-Niven numbers (A352508).
Original entry on oeis.org
144, 15630, 164862, 202761, 373788, 450189, 753183, 1403961, 1779105, 2588415, 2673774, 2814229, 2850880, 3009174, 3013722, 3045870, 3091023, 3702390, 3942519, 4042950, 4432128, 4725432, 4938348, 5718942, 5907312, 6268248, 6519615, 6592752, 6791379, 7095492, 8567802
Offset: 1
144 is a term since 144, 145, 146 and 147 are all divisible by the sum of the digits in their Catalan representation:
k A014418(k) A014420(k) k/A014420(k)
--- ---------- ---------- ------------
144 100210 4 36
145 100211 5 29
146 101000 2 73
147 101001 3 49
Similar sequences:
A141769,
A328211,
A328207,
A328215,
A330933,
A331824,
A334311,
A342429,
A344344,
A352092,
A352110,
A352345.
-
c[n_] := c[n] = CatalanNumber[n]; catNivQ[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; seq[count_, nConsec_] := Module[{cn = catNivQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {catNivQ[k]}]; k++]; s]; seq[5, 4]
A364219
Starts of runs of 4 consecutive integers that are Jacobsthal-Niven numbers (A364216).
Original entry on oeis.org
1, 42, 43, 2731, 11605, 13024, 14229, 25983, 39390, 45727, 46624, 47529, 60073, 96039, 111390, 131103, 132010, 133984, 134430, 140767, 148180, 148181, 148509, 174762, 174763, 187744, 197790, 237609, 247114, 266453, 275229, 287988, 312190, 330847, 354429, 370269
Offset: 1
Similar sequences:
A141769,
A328211,
A328207,
A328215,
A330933,
A331824,
A334311,
A342429,
A344344,
A352092,
A352110,
A352345,
A352511.
-
consecJacobsthalNiven[4*10^5, 4] (* using the function from A364217 *)
-
lista(4*10^5, 4) \\ using the function from A364217
A364382
Starts of runs of 4 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).
Original entry on oeis.org
1, 2, 3, 8, 9, 42, 43, 84, 85, 2730, 2731, 5460, 5461, 21864, 21865, 59477, 60073, 66303, 75048, 112509, 156607, 174762, 174763, 283327, 312190, 320768, 349524, 349525, 351570, 354429, 374589, 384039, 479037, 504510, 527103, 624040, 625470, 656829, 688830, 711423
Offset: 1
Similar sequences:
A141769,
A328211,
A328207,
A328215,
A330933,
A331824,
A334311,
A342429,
A344344,
A352092,
A352110,
A352345,
A352511,
A364219.
-
consecGreedyJN[72000, 4] (* using the function consecGreedyJN from A364380 *)
-
lista(10^5, 4) \\ using the function lista from A364380
A381584
Starts of runs of 4 consecutive integers that are all terms in A381581.
Original entry on oeis.org
1, 55, 2104, 5222, 24784, 63510, 64264, 69487, 95463, 121393, 184327, 327303, 374589, 463110, 468168, 561069, 572550, 596868, 671407, 740310, 759030, 819948, 902670, 956680, 1023009, 1036230, 1065030, 1259817, 1274910, 1359552, 1683154, 1714470, 1731750, 2182023
Offset: 1
1 is a term since A291711(1) = 1 divides 1, A291711(2) = 2 divides 2, A291711(3) = 1 divides 3, and A291711(4) = 2 divides 4.
55 is a term since A291711(55) = 1 divides 55, A291711(56) = 2 divides 56, A291711(57) = 3 divides 57, and A291711(58) = 2 divides 58.
-
f[n_] := f[n] = Fibonacci[2*n]; q[n_] := q[n] = Module[{s = 0, m = n, k}, While[m > 0, k = 1; While[m > f[k], k++]; If[m < f[k], k--]; If[m >= 2*f[k], s += 2; m -= 2*f[k], s++; m -= f[k]]]; Divisible[n, s]]; seq[count_, nConsec_] := Module[{cn = q /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {q[k]}]; k++]; s]; seq[12, 4]
-
mx = 20; fvec = vector(mx, i, fibonacci(2*i)); f(n) = if(n <= mx, fvec[n], fibonacci(2*n));
is1(n) = {my(s = 0, m = n, k); while(m > 0, k = 1; while(m > f(k), k++); if(m < f(k), k--); if(m >= 2*f(k), s += 2; m -= 2*f(k), s++; m -= f(k))); !(n % s);}
list(lim) = {my(q1 = is1(1), q2 = is1(2), q3 = is1(3), q4); for(k = 4, lim, q4 = is1(k); if(q1 && q2 && q3 && q4, print1(k-3, ", ")); q1 = q2; q2 = q3; q3 = q4);}
A364126
Starts of runs of 4 consecutive integers that are Stolarsky-Niven numbers (A364123).
Original entry on oeis.org
125340, 945591, 14998632, 16160505, 19304934, 42053801, 42064137, 46049955, 57180537, 103562368, 108489885, 122495982, 135562299, 139343337, 147991452, 164002374, 271566942, 296019657, 301748706, 310980030, 314537247, 316725570, 333478935, 336959907, 349815255
Offset: 1
Similar sequences:
A141769,
A328211,
A328207,
A328215,
A330933,
A331824,
A334311,
A342429,
A344344,
A352092,
A352110,
A352345,
A352511.
-
seq[2, 4] (* generates the first 2 terms, using the function seq[count, nConsec] from A364124 *)
-
lista(2, 4) \\ generates the first 2 terms, using the function lista(count, nConsec) from A364124
A363792
Starts of runs of 4 consecutive integers that are primitive binary Niven numbers (A363787).
Original entry on oeis.org
8255214, 14673870, 29092590, 33185646, 41743854, 47697390, 48069486, 56348622, 56999790, 58116078, 59604462, 60534702, 60813774, 61837038, 62581230, 64069614, 64999854, 65371950, 66581262, 66674286, 75232494, 83418606, 86767470, 88069806, 92255886, 95418702, 96441966, 99511758, 99604782
Offset: 1
8255214 is a term since 8255214, 8255215, 8255216 and 8255217 are all primitive binary Niven numbers.
-
binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; primBinNivQ[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]);
seq[kmax_] := Module[{quad = primBinNivQ /@ Range[4], s = {}, k = 5}, While[k < kmax, If[And @@ quad, AppendTo[s, k - 4]]; quad = Join[Rest[quad], {primBinNivQ[k]}]; k++]; s]; seq[3*10^7]
-
isbinniv(n) = !(n % hammingweight(n));
isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
lista(kmax) = {my(quad = vector(4, i, isprim(i)), k = 5); while(k < kmax, if(vecsum(quad) == 4, print1(k-4, ", ")); quad = concat(vecextract(quad, "^1"), isprim(k)); k++); }
A364009
Starts of runs of 4 consecutive integers that are Wythoff-Niven numbers (A364006).
Original entry on oeis.org
374, 978, 17708, 832037, 1631097, 4821894, 5572377, 13376142, 14808759, 14930343, 35406720, 36534357, 38208519, 38748444, 38890509, 39088166, 65375232, 70046899, 79988116, 81224637, 82071105, 82898100, 94109430, 94875417, 95070492, 98014500, 100350522, 101651787, 102190437
Offset: 1
Similar sequences:
A141769,
A328211,
A328207,
A328215,
A330933,
A331824,
A334311,
A342429,
A344344,
A352092,
A352110,
A352345,
A352511.
A331825
Positive numbers k such that -k, -(k + 1), -(k + 2), and -(k + 3) are 4 consecutive negative negabinary-Niven numbers (A331728).
Original entry on oeis.org
413, 2093, 3773, 4613, 7133, 7973, 8813, 10493, 11869, 15829, 16373, 23749, 30653, 31493, 34853, 35629, 37373, 39589, 40733, 49133, 51469, 54585, 55429, 63349, 64253, 65513, 67613, 70965, 75229, 91069, 98989, 102949, 103725, 106909, 110869, 114653, 129773, 131033
Offset: 1
-
negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; nConsec = 4; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[k]}]; k++]; seq
A338516
Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).
Original entry on oeis.org
1377595575, 4275143301, 13616091683, 13640596128, 15016388244, 15176619135, 21361749754, 23605084359, 24794290167, 28025464183, 29639590888, 30739547718, 33924433023, 35259630279, 38008366692, 38670247670, 38681191672, 40210059079, 40507412213, 49759198333, 52555068607
Offset: 1
1377595575 is a term since the 4 consecutive numbers from 1377595575 to 1377595578 are all terms of A093705.
-
divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[4]; Reap[Do[If[And @@ div, Sow[k - 4]]; div = Join[Rest[div], {divQ[k]}], {k, 5, 5*10^9}]][[2, 1]]
SequencePosition[Table[If[Mod[n,Total[Flatten[IntegerDigits[#,2]&/@Divisors[n]]]]==0,1,0],{n,526*10^8}],{1,1,1,1}][[;;,1]] (* The program will take a long time to run. *) (* Harvey P. Dale, May 28 2023 *)
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