Alois P. Heinz has authored 6539 sequences. Here are the ten most recent ones:
A385245
Primes that are no longer prime if in their binary representation any single bit is flipped but stay prime if a 1 bit is prepended.
Original entry on oeis.org
223, 257, 509, 787, 853, 877, 1259, 1451, 1973, 2917, 3511, 5099, 6287, 6521, 7841, 8171, 8923, 9319, 10567, 11353, 12517, 12637, 12763, 13687, 14107, 14629, 15217, 15607, 16943, 17519, 18089, 18593, 18743, 19139, 20183, 20393, 20639, 21701, 22943, 26591, 26891
Offset: 1
257 = 100000001_2 and 769 = 1100000001_2 are primes and 256, 259, 261, 265, 273, 289, 321, 385, 1 are not prime. So 257 is a term.
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q:= p-> (m-> andmap(isprime, [p, 2^(m+1)+p]) and not ormap
(i->isprime(Bits[Xor](p, 2^i)), [$0..m]))(ilog2(p)):
select(q, [$2..27000])[];
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Select[Prime[Range[3000]], PrimeQ[2^BitLength[#] + #] && NoneTrue[BitXor[#, 2^Range[0, BitLength[#] - 1]], PrimeQ] &] (* Paolo Xausa, Aug 05 2025 *)
A386247
Primes containing 000 as a substring.
Original entry on oeis.org
10007, 10009, 40009, 70001, 70003, 70009, 90001, 90007, 100003, 100019, 100043, 100049, 100057, 100069, 130003, 140009, 150001, 160001, 160009, 170003, 180001, 180007, 200003, 200009, 200017, 200023, 200029, 200033, 200041, 200063, 200087, 220009, 230003, 240007
Offset: 1
Cf.
A000040,
A164968,
A243527,
A166580,
A166581,
A166582,
A167281,
A131645,
A167282,
A167290,
A167292,
A386240.
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Select[Prime[Range[1230, 25000]], StringContainsQ[IntegerString[#], "000"] &] (* Paolo Xausa, Jul 19 2025 *)
A385413
Number of solid standard Young tableaux of 2n cells and height >= n.
Original entry on oeis.org
1, 3, 23, 261, 3787, 63395, 1191041, 24547919, 549727747, 13239969349, 340470351905, 9279758909457, 266461484866363
Offset: 0
A385408
Sum over all ordered partitions of [n] of 6^j for an ordered partition with j inversions.
Original entry on oeis.org
1, 1, 8, 388, 113480, 199246816, 2099255895008, 132708276995157568, 50336523318422432038400, 114556539064849604787867141376, 1564256035642651626332994903500876288, 128158392280785912677966097933268099449960448, 62999559569114394473388668602373642996554916532377600
Offset: 0
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b:= proc(o, u, t) option remember; `if`(u+o=0, 1, `if`(t=1,
b(u+o, 0$2), 0)+add(6^(u+j-1)*b(o-j, u+j-1, 1), j=1..o))
end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..14);
A385299
Number of Schröder paths of semilength 2n and having n valleys.
Original entry on oeis.org
1, 1, 11, 155, 2554, 46377, 899107, 18269407, 384577010, 8321452706, 184074021999, 4145999605431, 94799675260406, 2195442934642375, 51402741095491155, 1214975868437406375, 28956949406425290114, 695214262740084758154, 16800125921481031616230, 408354422827279445763942
Offset: 0
a(0) = 1: the empty path.
a(1) = 1: UDUD.
a(2) = 11: HUDUDUD, UUDDUDUD, UHDUDUD, UDUUDDUD, UUDUDDUD, UDUHDUD, UDUDUUDD, UDUUDUDD, UUDUDUDD, UDUDUHD, UDUDUDH.
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b:= proc(x, y, t, c) option remember; `if`(y<0 or y>x, 0,
`if`(x=0, `if`(c=0, 1, 0), b(x-1, y-1, 1, c+1)+
b(x-1, y+1, 0, c+1-4*t)+b(x-2, y, 0, c+2)))
end:
a:= n-> b(4*n, 0$3):
seq(a(n), n=0..19);
Original entry on oeis.org
2, 5, 13, 37, 101, 271, 727, 1931, 5003, 12547, 30449, 71761, 165037, 372149, 826303, 1813219, 3944921, 8533073, 18393821, 39588071, 85192381, 183479291, 395667617, 854417989, 1847225579, 3996807053, 8650687127, 18721431499, 40496966207, 87538925959, 189076973699
Offset: 0
A384498
Squarefree numbers whose distinct prime factors can be partitioned into two sets with equal sums.
Original entry on oeis.org
1, 30, 70, 286, 646, 1798, 2145, 2310, 2730, 3135, 3526, 3570, 4641, 4845, 5005, 5610, 6006, 6279, 6630, 7198, 7410, 7854, 8778, 8855, 8970, 9177, 10366, 10374, 10626, 10695, 11305, 11571, 11730, 13110, 13485, 13566, 13585, 15470, 16095, 16302, 16422, 16530
Offset: 1
2145 = 3*5*11*13 is a term because it is squarefree and 3+13 = 5+11.
16422 = 2*3*7*17*23 is squarefree and 2+7+17 = 3+23.
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q:= n-> (l-> {l[.., 2][]} minus {1}={} and (s->
(m-> m::even and coeff(mul(1+x^j, j=s), x, m/2)>0)
(add(i, i=s)))({l[.., 1][]}))(ifactors(n)[2]):
select(q, [$1..20000])[];
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Join[{1},Select[Range[16600],SquareFreeQ[#]&&MemberQ[Total/@Subsets[First/@FactorInteger[#]],Total[First/@FactorInteger[#]]/2]&]] (* James C. McMahon, Jun 02 2025 *)
A384368
Number of permutations of [2n] with n inversions.
Original entry on oeis.org
1, 1, 5, 29, 174, 1068, 6655, 41926, 266338, 1703027, 10947079, 70673825, 457927079, 2976282415, 19395654894, 126688273871, 829176461458, 5436687172806, 35703722618623, 234807844921153, 1546217013188447, 10193761267335877, 67275841673522196, 444431529264364506
Offset: 0
a(0) = 1: the empty permutation.
a(1) = 1: 21.
a(2) = 5: 1342, 1423, 2143, 2314, 3124.
a(3) = 29: 123654, 124563, 124635, 125364, 125436, 126345, 132564, 132645, 134265, 134526, 135246, 142365, 142536, 143256, 152346, 213564, 213645, 214365, 214536, 215346, 231465, 231546, 234156, 241356, 312465, 312546, 314256, 321456, 412356.
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a:= n-> coeff(series(mul((1-q^j)/(1-q), j=1..2*n), q, n+1), q, n):
seq(a(n), n=0..23);
A382780
Sum of the orders of all permutations of [n] with distinct cycle lengths.
Original entry on oeis.org
1, 1, 2, 12, 48, 360, 2520, 22680, 221760, 2298240, 28425600, 385862400, 5269017600, 80951270400, 1347631084800, 21565729785600, 413922526617600, 8409043612569600, 172028224598630400, 3765253760710041600, 84080417596471296000, 1935910813364656128000
Offset: 0
a(3) = 12 = 2+2+2+3+3: (1)(23), (13)(2), (12)(3), (123), (132).
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b:= proc(n, i, m) option remember; `if`(i*(i+1)/2 b(n$2, 1):
seq(a(n), n=0..22);
A382781
Sum of GCD of cycle lengths over all permutations of [n] with distinct cycle lengths.
Original entry on oeis.org
0, 1, 2, 9, 32, 170, 1164, 7434, 62880, 582336, 5875200, 60041520, 841501440, 9440926560, 141618778560, 2222190784800, 34862691548160, 543348318159360, 11173101312844800, 186494289764106240, 4219768887634944000, 86094733814301542400, 1834643656963469721600
Offset: 0
a(3) = 9 = 3+3+1+1+1: (123), (132), (1)(23), (13)(2), (12)(3).
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b:= proc(n, i, m) option remember; `if`(i*(i+1)/2 b(n$2, 0):
seq(a(n), n=0..22);
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