Search: a169887 -id:a169887
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A169906
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Carryless products 2*A169887, sorted and duplicates removed.
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+20
1
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2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 204, 206, 222, 224, 246, 248, 266, 268, 282, 284, 402, 408, 422, 426, 444, 448, 464, 468, 482, 486, 602, 608, 624, 628, 642, 646, 662, 666, 684, 688, 804, 806, 826, 828, 842, 844, 862
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OFFSET
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1,1
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COMMENTS
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Carryless doubles of the carryless primes.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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42, 46, 40, 44, 48, 82, 86, 80, 84, 88, 2, 4, 6, 8, 2, 4, 6, 8, 22, 26, 20, 24, 28, 62, 66, 60, 64, 68, 402, 408, 444, 448, 482, 486, 422, 426, 464, 468, 806, 804, 842, 844, 886, 888, 826, 828, 862, 864, 2, 6, 4, 8, 206, 204, 246, 248, 282, 284, 222, 224, 266, 268, 602, 608
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OFFSET
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1,1
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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405, 429, 441, 461, 489, 501, 504, 506, 509, 605, 621, 649, 669, 681, 40401, 40601, 42041, 42229, 44021, 44869, 46081, 46849, 48061, 48289, 50501, 50509, 60409, 60609, 62049, 62821, 64029, 64261, 66089, 66241, 68069, 68881
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internal format)
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OFFSET
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1,1
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LINKS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A169884
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Numbers consisting of either all even digits or just 5's and 0's.
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+10
6
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0, 2, 4, 5, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 50, 55, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 244, 246, 248, 260, 262, 264, 266, 268, 280, 282, 284, 286, 288, 400, 402, 404, 406
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OFFSET
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1,2
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COMMENTS
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These are all the divisors of zero in carryless arithmetic mod 10. E.g. 5 * 44 = 0.
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LINKS
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MATHEMATICA
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With[{upto=410}, Select[Union[Join[Select[Range[upto], And@@EvenQ[ IntegerDigits[#]]&], FromDigits/@Tuples[{5, 0}, Ceiling[Log[ 10, upto]]]]], #<=upto&]] (* Harvey P. Dale, Aug 05 2011 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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A163396
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Primes in carryless arithmetic mod 10 in which all digits except the rightmost are even.
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+10
5
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21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 201, 209, 227, 229, 241, 243, 261, 263, 287, 289, 403, 407, 421, 427, 443, 449, 463, 469, 481, 487, 603, 607, 623, 629, 641, 647, 661, 667, 683, 689, 801, 809, 821
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OFFSET
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1,1
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COMMENTS
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These are called e-type primes.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A169984
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Primes in carryless arithmetic mod 10 in which all digits except the rightmost are zero or five.
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+10
5
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51, 52, 53, 54, 56, 57, 58, 59, 551, 553, 557, 559, 5051, 5053, 5057, 5059, 5501, 5503, 5507, 5509, 50051, 50053, 50057, 50059, 55001, 55003, 55007, 55009, 55551, 55553, 55557, 55559, 500501, 500503, 500507, 500509, 505001, 505003
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OFFSET
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1,1
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COMMENTS
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These are called f-type primes.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A169903
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Primitive primes in carryless arithmetic mod 10.
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+10
2
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21, 23, 25, 27, 29, 51, 56, 201, 209, 227, 229, 241, 243, 261, 263, 287, 289, 551, 2023, 2027, 2043, 2047, 2061, 2069, 2081, 2089, 2207, 2209, 2221, 2223, 2263, 2267, 2281, 2287, 2401, 2407, 2421, 2423, 2441, 2449, 2483, 2489, 2603, 2609
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OFFSET
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1,1
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COMMENTS
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Define the units in carryless arithmetic mod 10 to be the numbers 1, 3, 7 and 9 (these divide any number). A prime is a number N, not a unit, whose only factorizations are of the form N = u * M, where u is a unit.
A prime is primitive if it not the carryless product of a smaller prime and a unit.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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A169962
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Number of n-digit primes in carryless arithmetic mod 10.
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+10
1
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0, 0, 28, 44, 168, 612, 2520, 10356, 44712, 195120, 868224, 3905388, 17756424, 81376140, 375603480, 1743843924, 8138028696, 38146891320, 179515196280, 847710124128, 4015470916296, 19073484584388, 90826125756552, 433488317523588, 2073205037124648
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OFFSET
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0,3
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LINKS
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FORMULA
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For formula see Maple code.
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MAPLE
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with(numtheory); f:=proc(n) local t1, d; if n <= 1 then RETURN(0); fi; t1:=0; for d from 1 to n-1 do if n-1 mod d = 0 then t1:=t1+(4/(n-1))*mobius((n-1)/d)*(2^d+5^d); fi; od: t1; end;
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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