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A325097 Heinz numbers of integer partitions whose distinct parts have no binary carries. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 38, 41, 42, 43, 47, 48, 49, 52, 53, 54, 56, 57, 58, 59, 61, 63, 64, 67, 69, 71, 72, 73, 74, 76, 79, 81, 83, 84, 86, 89, 95, 96, 97, 98, 99, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary digits.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose distinct prime indices have no binary carries.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

Most small numbers are in the sequence, however the sequence of non-terms together with their prime indices begins:

  10: {1,3}

  15: {2,3}

  20: {1,1,3}

  22: {1,5}

  30: {1,2,3}

  34: {1,7}

  39: {2,6}

  40: {1,1,1,3}

  44: {1,1,5}

  45: {2,2,3}

  46: {1,9}

  50: {1,3,3}

  51: {2,7}

  55: {3,5}

  60: {1,1,2,3}

  62: {1,11}

  65: {3,6}

  66: {1,2,5}

  68: {1,1,7}

  70: {1,3,4}

MATHEMATICA

binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

Select[Range[100], stableQ[PrimePi/@First/@FactorInteger[#], Intersection[binpos[#1], binpos[#2]]!={}&]&]

CROSSREFS

Cf. A000110, A000720, A001222, A050315, A056239, A080572, A112798, A247935.

Cf. A325094, A325095, A325096, A325097, A325098, A325100, A325102, A325103.

Sequence in context: A191878 A122154 A122156 * A030700 A305933 A105208

Adjacent sequences:  A325094 A325095 A325096 * A325098 A325099 A325100

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 27 2019

STATUS

approved

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)