A205406 - OEIS

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A205406

a(n) = s(k)-s(j), where (k,j) is the least pair for which n divides s(k)-s(j), and s(j) = floor((j+1)^2/2)/2.

1, 2, 3, 4, 5, 6, 7, 8, 18, 10, 11, 12, 13, 14, 15, 16, 34, 18, 19, 20, 21, 22, 23, 24, 50, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 98, 50, 51, 52, 106, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 201, 68

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

OFFSET

1,2

COMMENTS

For a guide to related sequences, see A204892.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12004

FORMULA

a(n) = n * A198293(n). - Antti Karttunen, Dec 05 2021

EXAMPLE

The least k such that 9 divides s(k)-s(j) for some k is k=8, for which j=2: s(8)-s(2) = 20-2 = 18, so a(9)=18.

MATHEMATICA

(See the program at A205402.)

s[m_]:=s[m]=Floor[(m+1)^2/2]/2

A205406[n_]:=(k=2; found=False; While[!found, Do[If[Mod[d=s[k]-s[j], n]==0, found=True; Break[]], {j, k-1}]; k++]; d)

nterms=100; Table[A205406[n], {n, nterms}] (* Paolo Xausa, Dec 03 2021 *)

PROG

(PARI)

A002620(n) = ((n^2)>>2);

A002620shiftedleft(n) = A002620(1+n);

A205406(n) = { my(d); for(k=2, oo, for(j=1, k-1, if(!((d=A002620shiftedleft(k)-A002620shiftedleft(j))%n), return(d)))); }; \\ Antti Karttunen, Dec 05 2021

CROSSREFS

Cf. A002620, A198293, A205402, A204892.

Sequence in context: A140576 A200447 A274840 * A066759 A204928 A171723

Adjacent sequences: A205403 A205404 A205405 * A205407 A205408 A205409

KEYWORD

nonn,look

AUTHOR

Clark Kimberling, Jan 27 2012

EXTENSIONS

Definition corrected by Clark Kimberling, Dec 05 2021

STATUS

approved