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 A291460 Even numbers n such that the decimal expansion of n contains the decimal expansion of the greatest odd divisor of n as a substring. 2
 16, 128, 384, 512, 1024, 1536, 1792, 2176, 2560, 2912, 3072, 5120, 7168, 8192, 9216, 11264, 13312, 15360, 15616, 16384, 17408, 19456, 21504, 23552, 25600, 27648, 28672, 29696, 31744, 33792, 35840, 37376, 37888, 39936, 41984, 43392, 57344, 66560, 90112, 98304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 43392 and 443392 are both in this sequence because 43392 = 2^7*339 and 443392 = 2^10*433. Removing the first digit of 443392 gives 43392. Are there any other numbers in this sequence such that removing the first digit gives another number in the sequence? Every number of the form 29090...90912 is in this sequence because 2912 = 2^5*91, 290912 = 2^5*9091, 29090912 = 2^5*909091, and so on. Sequence is infinite since it contains infinite subsequences, like the numbers of the form 7*2^(20*k-5) for k>0. - Giovanni Resta, Aug 25 2017 Trivially all powers of two which contain the digit 1 are members, see A035057. - Robert G. Wilson v, Aug 25 2017 Number of terms less than 10^k: 0, 1, 4, 15, 40, 57, 76, 108, 146, 194, 258, 336, 447, etc. - Robert G. Wilson v, Aug 25 2017 LINKS Giovanni Resta, Table of n, a(n) for n = 1..1567 (terms < 10^20) EXAMPLE The greatest odd divisor of 1792 = 2^8*7 is 7, which is in 1(7)92. Therefore, 1792 is in this sequence. 2^10*x = 1024*x contains x as a substring for all x from 1 to 41. Therefore, 1024*x is in this sequence for all odd x from 1 to 41. MAPLE with(numtheory): 2*select(n->searchtext("".(max(op(select(type, divisors(2*n), odd)))), "".(2*n))>0, [\$1..50000]); # Paolo P. Lava, Sep 05 2018 MATHEMATICA inQ[n_] := StringPosition[ToString[n], ToString[n/2^IntegerExponent[n, 2]]] != {}; Select[2 Range[50000], inQ] (* Giovanni Resta, Aug 24 2017 and slightly modified by Robert G. Wilson v, Aug 25 2017 *) PROG (PARI) is(n)=if(n%2, return(0)); my(r=n>>valuation(n, 2), m=Mod(r, 10^#digits(r))); while(n>=r, if(n==m, return(1)); n\=10); 0 \\ Charles R Greathouse IV, Aug 26 2017 (Python) A291460_list = [2*x for x in range(1, 10**6) if str(int(bin(x).rstrip('0'), 2)) in str(2*x)] # Chai Wah Wu, Aug 31 2017 CROSSREFS Cf. A000265, A035057, A291555. Sequence in context: A133111 A268998 A253319 * A004017 A167471 A153115 Adjacent sequences:  A291457 A291458 A291459 * A291461 A291462 A291463 KEYWORD base,nonn AUTHOR Bobby Jacobs, Aug 24 2017 EXTENSIONS More terms from Giovanni Resta, Aug 24 2017 Name edited by Felix FrÃ¶hlich, Aug 24 2017 STATUS approved

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Last modified August 9 17:13 EDT 2022. Contains 356026 sequences. (Running on oeis4.)