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A275340
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Nontrivial centered polygonal numbers: numbers of the form A101321(n,k) where n >= 1 and k >= 2.
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4
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4, 7, 10, 11, 13, 16, 19, 21, 22, 25, 28, 29, 31, 34, 37, 40, 41, 43, 46, 49, 51, 52, 55, 56, 57, 58, 61, 64, 67, 70, 71, 73, 76, 79, 81, 82, 85, 88, 91, 92, 94, 97, 100, 101, 103, 106, 109, 111, 112, 113, 115, 118, 121, 124, 127, 130, 131, 133, 136, 137, 139, 141, 142, 145, 148, 151
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This is a centered polygonal number analog to A090466.
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LINKS
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FORMULA
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MAPLE
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isA275340 := proc(n)
local nsearch, ksearch;
for nsearch from 1 do
return false;
end if;
for ksearch from 2 do
if A101321(nsearch, ksearch) = n then
return true;
elif A101321(nsearch, ksearch) > n then
break;
end if;
end do:
end do:
end proc:
for n from 1 to 400 do
if isA275340(n) then
printf("%d, ", n) ;
end if;
end do:
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MATHEMATICA
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maxTerm = 1000;
Table[1+n*k*(k+1)/2, {n, 1, maxTerm-1}, {k, 2, Sqrt[2maxTerm] // Ceiling}] // Flatten // Union // Select[#, # <= maxTerm&]& (* Jean-François Alcover, Jun 17 2023 *)
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PROG
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(PARI) list(lim)=my(v=List(), t); lim\=1; for(k=2, sqrt(8*lim-7)/2, t=k*(k+1)/2; forstep(a=t+1, lim, t, listput(v, a))); Set(v) \\ Charles R Greathouse IV, Jul 28 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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