A075799 -id:A075799 - cp's OEIS frontend

A075800 Palindromic numbers which are products of an odd number of distinct primes.

2, 3, 5, 7, 11, 66, 101, 131, 151, 181, 191, 222, 282, 313, 353, 373, 383, 434, 474, 494, 555, 595, 606, 646, 727, 757, 777, 787, 797, 919, 929, 969, 1001, 1221, 1551, 1771, 2222, 2882, 3333, 3553, 4334, 4994, 5335, 5555, 5665, 5885, 5995, 6006, 6226, 6446, 6886

Offset: 1

Jani Melik, Oct 13 2002

			191 is palindromic and prime, 222=2*3*37 is palindromic and a product of 3 distinct primes.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A002385, A069217, A032350, A030059, A075799, A075806 (first differences).

test := proc(n) local d; d := convert(n,base,10); return ListTools[Reverse](d)=d and numtheory[mobius](n)=-1; end; a := []; for n from 1 to 7000 do if test(n) then a := [op(a),n]; end; od; a;

Select[Range[10000], PalindromeQ[#] && MoebiusMu[#] == -1 &] (* Paolo Xausa, Mar 10 2025 *)

Edited by Dean Hickerson, Oct 21 2002

A075805 Differences between adjacent palindromic numbers which are products of an even number of distinct primes.

Original entry on oeis.org

5, 16, 11, 22, 22, 34, 30, 20, 41, 60, 41, 20, 70, 61, 51, 10, 20, 10, 20, 61, 81, 10, 20, 30, 51, 20, 20, 20, 20, 41, 10, 10, 20, 10, 122, 330, 220, 330, 11, 440, 561, 110, 110, 220, 440, 891, 231, 110, 1551, 451, 330, 550, 1122, 110, 220, 552, 100, 300, 400, 100

Offset: 1

Jani Melik, Oct 13 2002

			a(1)=6-1=5, a(2)=22-6=16.

Paolo Xausa, Table of n, a(n) for n = 1..1000

Cf. A037010.

First differences of A075799.

test := proc(n) local d; d := convert(n,base,10); return ListTools[Reverse](d)=d and numtheory[mobius](n)=1; end; s := []; for n from 1 to 11000 do if test(n) then s := [op(s),n]; end; od; a := [op(2..-1,s)-op(1..-2,s)];

Differences[Select[Range[10000], PalindromeQ[#] && MoebiusMu[#] == 1 &]] (* Paolo Xausa, Mar 10 2025 *)

Edited by Dean Hickerson, Oct 21 2002

cp's OEIS Frontend

A075800 Palindromic numbers which are products of an odd number of distinct primes.

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