Johan Särnbratt - cp's OEIS frontend

A192734 Smallest number having binary weight of 3 and n distinct prime factors.

7, 21, 273, 16401, 1048593, 4295032833, 1099512676353, 9007199256838145, 302231455185132270387201, 1208944266358702884257793, 1329227995784915872903807060297121793, 1393796574908163946347162983661240005427201

Offset: 1

Johan Särnbratt, Jul 08 2011

Written in binary, these numbers have exactly three 1 bits and the other bits are all 0's. This means that these numbers are of the sum of 1 plus two larger distinct powers of 2. - Alonso del Arte, Jul 08 2011
a(n) > A002110(n). [Reinhard Zumkeller, Jul 09 2011]
Sequence is not monotone: a(12) > a(13). [Charles R Greathouse IV, Jul 11 2011]

Charles R Greathouse IV, Table of n, a(n) for n = 1..14

Cf. A084468, A001221.

a192734 n = head [x | x <- [2^u + 2^v + 1 | u <- [2..], v <- [1..u-1]],
                      a001221 x == n]
-- Reinhard Zumkeller, Jun 14 2015, Jul 09 2011

list = {7}; For[max = 1; n = 2, n < 120,
For[m = 0, m < n,
  tal = 2*(2^n + 2^m) + 1; num = PrimeNu[tal];
  If[num > max, AppendTo[list, tal]; max = num]
  , m++], n++] (* Sarnbratt *)
A084468 = Flatten[Table[2^m + 2^n + 1, {m, 2, 80}, {n, m - 1}]]; Flatten[Table[Take[Select[A084468, PrimeNu[#] == n &], 1], {n, 10}]] (* Alonso del Arte, Jul 08 2011 *)

a(n)={
  my(t);
  for(a=2,9e9,
    t=1+1<Charles R Greathouse IV, Jul 08 2011

a(9) corrected by Charles R Greathouse IV, Jul 08 2011

a(12) from Charles R Greathouse IV, Jul 11 2011

A159078 Number of perfect powers with distinct digits in base n.

Original entry on oeis.org

1, 1, 9, 8, 25, 50, 88, 297, 657, 1418, 3212, 8662, 24185, 64103, 183718

Offset: 2

Johan Särnbratt, Apr 04 2009

			The 8 powers with unique digits in base 5 are 1, 4, 8, 9, 16, 27, 144, and 576; in base 5 these are 1, 4, 13, 14, 31, 102, 1304, and 4301.

Cf. A075309

okdigs(digs) = {for (i = 1, #digs-1, for (j = i+1, #digs, if (digs[j] == digs[i], return (0);););); return (1);}
a(n) = {b = n; sols = Set([1]); vmax = b^b; pmax = ceil(log(vmax)/log(2)); for (p = 2, pmax, i = 2; while ((iep = i^p) < vmax, if (okdigs(digits(iep, b)), sols = Set(concat(sols, iep));); i++;);); #sols;} \\ Michel Marcus, Aug 19 2013

a(11) - a(16) from Johan Särnbratt, Apr 21 2009

A161020 All the non-repdigit terms of A160818.

Original entry on oeis.org

370, 407, 481, 518, 592, 629, 370370, 407407, 481481, 518518, 592592, 629629, 370370370, 407407407, 456790123, 469135802, 481481481, 493827160, 506172839, 518518518, 530864197, 543209876, 592592592, 629629629, 370370370370

Offset: 1

Johan Särnbratt, Jun 02 2009

All known terms are multiples of 111/3 = 37.

Non-repdigit numbers n such that ((10^A055642(n)-1)/9)*(A007953(n)/A055642(n)) = n. So the sequence is infinite. - Altug Alkan, Sep 05 2016

			For example with 370: (073+037+307+370+703+730)/6 = 370.

Cf. A160818, A275772, A275945.

read("transforms3") ; isrep := proc(n) if nops(convert(convert(n,base,10),set)) = 1 then true; else false; fi; end: a160818 := BFILETOLIST("b160818.txt") ; for i from 1 to 400 do a := op(i,a160818) ; if not isrep(a) then printf("%d,",a) ; fi; od: # R. J. Mathar, Jul 04 2009

More terms from R. J. Mathar, Jul 04 2009

A136332 a(n) is the smallest term appearing after a(n-1) in A067581.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 29, 31, 32, 35, 36, 37, 38, 39, 43, 48, 49, 53, 54, 55, 56, 65, 67, 75, 76, 77, 78, 86, 87, 88, 89, 95, 96, 97, 98, 99, 106, 107, 108, 109, 110, 111, 112, 120, 123, 132, 192, 210, 212, 213, 231, 251, 312, 318, 319, 321, 324

Offset: 1

Johan Särnbratt, Mar 27 2008

			a(13) = 21 because 21 is the lowest term appearing after 12 in A067581

Cf. A067581.

A139803 A033875(n) + 2^a(n) = A033875(n+1).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 2, 3, 4, 5, 2, 7, 4, 1, 2, 3, 4, 9, 2, 955, 468

Offset: 1

Johan Särnbratt, May 22 2008

a(23) > 10^4. - Zak Seidov, Jan 24 2017

a(23) > 30000 (if it exists). - Pontus von Brömssen, Jan 08 2023

			a(10) = 4 because A033875(10) = 31, 31 + 2^4 = 47, which is prime.

Skipping from prime to prime by least powers of 2: A033875.

Cf. A059662, A067760.

p = 2; n = 0; While[true, x = 0; While[ ! PrimeQ[p + 2^x], x++ ]; p = p + 2^x; Print[x]; n++ ]

a(n) = A067760((A033875(n)-1)/2) for n >= 2. - Pontus von Brömssen, Jan 08 2023

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User: Johan Särnbratt

A192734 Smallest number having binary weight of 3 and n distinct prime factors.

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A159078 Number of perfect powers with distinct digits in base n.

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A161020 All the non-repdigit terms of A160818.

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A136332 a(n) is the smallest term appearing after a(n-1) in A067581.

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A139803 A033875(n) + 2^a(n) = A033875(n+1).

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