A297646 -id:A297646

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A297644

Pentagonal numbers (A000326) in which parity of digits alternates.

+10
4

1, 5, 12, 70, 92, 145, 210, 852, 925, 2147, 2501, 3290, 3432, 3876, 4187, 4347, 6305, 6501, 12105, 12927, 25676, 27270, 27676, 45850, 58707, 69230, 69876, 70525, 76501, 78547, 98945, 101270, 123410, 161212, 270725, 349692, 367290, 567030, 707610, 709672

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Intersection of A000326 and A030141. - Felix Fröhlich, Jan 03 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..2000

EXAMPLE

3876 is in the sequence because 3, 8, 7 and 6 have odd and even parity alternately.

MAPLE

filter:= proc(n) local L;

if n < 10 then return true fi;

L:= convert(n, base, 10) mod 2;

not has(L[2..-1]-L[1..-2], 0)

end proc:

select(filter, [seq(n*(3*n-1)/2, n=1..1000)]); # Robert Israel, Jan 03 2018

PROG

(PARI)

is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)

select(is_alt, vector(1000, n, (3*n^2-n)/2))

CROSSREFS

Cf. A297645, A297646, A297647.

Cf. A000326, A030141, A030152, A030160, A068882.

KEYWORD

nonn,base

AUTHOR

Colin Barker, Jan 02 2018

STATUS

approved

A297645

Hexagonal numbers (A000384) in which parity of digits alternates.

+10
4

1, 6, 45, 276, 325, 496, 561, 630, 703, 2145, 2701, 6903, 8385, 10585, 14365, 18721, 25878, 38503, 47278, 74305, 89676, 90525, 107416, 109278, 147696, 149878, 210925, 254541, 303810, 345696, 349030, 383250, 454581, 527878, 561270, 674541, 705078, 709836

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Intersection of A000384 and A030141. - Felix Fröhlich, Jan 03 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

EXAMPLE

6903 is in the sequence because 6, 9, 0 and 3 have even and odd parity alternately.

MAPLE

filter:= proc(n) local L;

if n < 10 then return true fi;

L:= convert(n, base, 10) mod 2;

not has(L[2..-1]-L[1..-2], 0)

end proc:

select(filter, [seq(n*(2*n-1), n=1..10^4)]); # Robert Israel, Jan 05 2018

PROG

(PARI)

is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)

select(is_alt, vector(1000, n, (4*n^2-2*n)/2))

CROSSREFS

Cf. A297644, A297646, A297647.

Cf. A000384, A030141, A030152, A030160, A068882.

KEYWORD

nonn,base

AUTHOR

Colin Barker, Jan 02 2018

STATUS

approved

A297647

Octagonal numbers (A000567) in which parity of digits alternates.

+10
4

1, 8, 21, 65, 96, 341, 3816, 4961, 8321, 8965, 9296, 10325, 12545, 14145, 14981, 16725, 18565, 23056, 27456, 36741, 63656, 65416, 103416, 105656, 169456, 181056, 210145, 216545, 232965, 236321, 256961, 412181, 430165, 434721, 569416, 614721, 658945, 698901

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Intersection of A000567 and A030141. - Felix Fröhlich, Jan 03 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..2000

EXAMPLE

8321 is in the sequence because 8, 3, 2 and 1 have even and odd parity alternately.

MAPLE

filter:= proc(n) local L;

if n < 10 then return true fi;

L:= convert(n, base, 10) mod 2;

not has(L[2..-1]-L[1..-2], 0)

end proc:

select(filter, [seq(n*(3*n-2), n=1..1000)]); # Robert Israel, Jan 03 2018

PROG

(PARI)

is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)

select(is_alt, vector(1000, n, (6*n^2-4*n)/2))

CROSSREFS

Cf. A297644, A297645, A297646.

Cf. A000567, A030141, A030152, A030160, A068882.

KEYWORD

nonn,base

AUTHOR

Colin Barker, Jan 02 2018

STATUS

approved

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