A385703 -id:A385703 - cp's OEIS frontend

A385700 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 4.

0, 4, 8, 21, 23, 25, 27, 29, 40, 42, 44, 46, 48, 61, 63, 65, 67, 69, 80, 82, 84, 86, 88, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269

Offset: 1

Stefano Spezia, Jul 07 2025

			263 is a term since 632 = 158*4 is divisible by 4.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Similar sequences for k=1..9: A001477, A273892, A008585, this sequence, A217398, A385701, A385702, A385703, A008591.

Select[Range[0,270],Divisible[FromDigits[RotateLeft[IntegerDigits[#]]],4] &]

isok(k) = if (k==0, return(1)); my(d=digits(k), v = vector(#d-1, i, d[i+1])); v = concat(v, d[1]); fromdigits(v) % 4 == 0; \\ Michel Marcus, Jul 08 2025

def ok(n): return int((s:=str(n))[1:]+s[0])%4 == 0
print([k for k in range(270) if ok(k)]) # Michael S. Branicky, Jul 08 2025

A385701 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 6.

Original entry on oeis.org

0, 6, 21, 24, 27, 42, 45, 48, 60, 63, 66, 69, 81, 84, 87, 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, 234, 237, 240, 243, 246, 249, 252, 255, 258, 261, 264, 267, 270, 273, 276, 279, 282, 285, 288, 291, 294, 297, 402, 405, 408, 411, 414, 417, 420, 423, 426, 429

Offset: 1

Stefano Spezia, Jul 07 2025

			426 is a term since 264 = 44*6 is divisible by 6.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Similar sequences for k=1..9: A001477, A273892, A008585, A385700, A217398, this sequence, A385702, A385703, A008591.

Select[Range[0,430],Divisible[FromDigits[RotateLeft[IntegerDigits[#]]],6] &]

isok(k) = if (k==0, return(1)); my(d=digits(k), v = vector(#d-1, i, d[i+1])); v = concat(v, d[1]); fromdigits(v) % 6 == 0; \\ Michel Marcus, Jul 08 2025

def ok(n): return int((s:=str(n))[1:]+s[0])%6 == 0
print([k for k in range(430) if ok(k)]) # Michael S. Branicky, Jul 08 2025

A385702 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 7.

Original entry on oeis.org

0, 7, 12, 19, 24, 36, 41, 48, 53, 65, 70, 77, 82, 89, 94, 102, 109, 116, 123, 130, 137, 144, 151, 158, 165, 172, 179, 186, 193, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 306, 313, 320, 327, 334, 341, 348, 355, 362, 369, 376, 383, 390, 397

Offset: 1

Stefano Spezia, Jul 07 2025

			376 is a term since 763 = 109*7 is divisible by 7.

Stefano Spezia, Table of n, a(n) for n = 1..10000

Similar sequences for k=1..9: A001477, A273892, A008585, A385700, A217398, A385701, this sequence, A385703, A008591.

Select[Range[0,400],Divisible[FromDigits[RotateLeft[IntegerDigits[#]]],7] &]

isok(k) = if (k==0, return(1)); my(d=digits(k), v = vector(#d-1, i, d[i+1])); v = concat(v, d[1]); fromdigits(v) % 7 == 0; \\ Michel Marcus, Jul 08 2025

def ok(n): return int((s:=str(n))[1:]+s[0])%7 == 0
print([k for k in range(400) if ok(k)]) # Michael S. Branicky, Jul 08 2025

cp's OEIS Frontend

A385700 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 4.

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A385701 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 6.

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A385702 Numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 7.

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Author

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Examples

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Programs

Mathematica

PARI

Python