A385779 -id:A385779 - cp's OEIS frontend

A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Clark Kimberling, Jul 11 2025

nonn

			First 20 triples:
  u    v    w
  6   11    6
  7   14    8
  8   17   10
  8   19   12
  9   20   12
  9   23   15
  9   26   24
 10   23   14
 10   27   18
 10   29   20
 10   31   30
 11   26   16
 11   31   21
 11   34   24
 11   36   36
 11   38   40
 12   29   18
 12   35   24
 12   39   28
 12   41   30

Cf. A385779, A386287, A386288.

z = 140;
t = Table[{b + c + d, c  d + d  b + b  c, b  c  d}, {b, 1, z - 2}, {c, b + 1, z - 1}, {d, c + 1, z}];
t1 = Union[Flatten[t, 2]];
t2 = Take[t1, 20]
Grid[t2]

A386031 Primes having only {0, 1, 5, 6} as digits.

Original entry on oeis.org

5, 11, 61, 101, 151, 601, 661, 1051, 1061, 1151, 1511, 1601, 5011, 5051, 5101, 5501, 5651, 6011, 6101, 6151, 6551, 6661, 10061, 10111, 10151, 10501, 10601, 10651, 11161, 11551, 15061, 15101, 15161, 15511, 15551, 15601, 15661, 16001, 16061, 16111, 16561, 16651

Offset: 1

Jason Bard, Jul 14 2025

Primes with decimal digits only in the set {0,1} mod 5.

Supersequence of A199325, A199326, A385779.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 5, 6]];

Select[FromDigits/@Tuples[{0,1,5,6},5],PrimeQ]

primes_with(, 1, [0, 1, 5, 6]) \\ uses function in A385776

print(list(islice(primes_with("0156"), 41))) # uses function/imports in A385776

Mathematica program corrected by Harvey P. Dale, Aug 27 2025

A386095 Primes having only {1, 2, 5, 6} as digits.

Original entry on oeis.org

2, 5, 11, 61, 151, 211, 251, 521, 661, 1151, 1511, 1621, 2111, 2161, 2221, 2251, 2521, 2551, 2621, 5261, 5521, 5651, 6121, 6151, 6211, 6221, 6521, 6551, 6661, 11161, 11251, 11261, 11551, 11621, 12161, 12211, 12251, 12511, 12611, 15121, 15161, 15511, 15551, 15661

Offset: 1

Jason Bard, Jul 16 2025

Supersequence of A385773, A385774, A385779.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 2, 5, 6]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 2, 5, 6}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 2, 5, 6]) \\ uses function in A385776

print(list(islice(primes_with("1256"), 41))) # uses function/imports in A385776

A386110 Primes having only {1, 3, 5, 6} as digits.

Original entry on oeis.org

3, 5, 11, 13, 31, 53, 61, 113, 131, 151, 163, 311, 313, 331, 353, 563, 613, 631, 653, 661, 1151, 1153, 1163, 1361, 1511, 1531, 1553, 1613, 1663, 3163, 3313, 3331, 3361, 3511, 3533, 3613, 3631, 5113, 5153, 5333, 5351, 5531, 5563, 5651, 5653, 6113, 6131, 6133, 6151

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A260224, A260225, A385777, A385779.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 3, 5, 6]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 3, 5, 6}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 3, 5, 6]) \\ uses function in A385776

print(list(islice(primes_with("1356"), 41))) # uses function/imports in A385776

A386119 Primes having only {1, 4, 5, 6} as digits.

Original entry on oeis.org

5, 11, 41, 61, 151, 461, 541, 641, 661, 1151, 1451, 1511, 4111, 4441, 4451, 4561, 4651, 5441, 5641, 5651, 6151, 6451, 6551, 6661, 11161, 11411, 11551, 14411, 14461, 14551, 14561, 15161, 15451, 15461, 15511, 15541, 15551, 15641, 15661, 16111, 16141, 16411, 16451

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A260268, A260269, A385779.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 4, 5, 6]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 4, 5, 6}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 4, 5, 6]) \\ uses function in A385776

print(list(islice(primes_with("1456"), 41))) # uses function/imports in A385776

A386129 Primes having only {1, 5, 6, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 61, 67, 71, 151, 157, 167, 557, 571, 577, 617, 661, 677, 751, 757, 761, 1117, 1151, 1171, 1511, 1567, 1571, 1657, 1667, 1777, 5167, 5171, 5557, 5651, 5657, 5711, 5717, 6151, 6551, 6571, 6577, 6661, 6761, 7151, 7177, 7517, 7561, 7577, 7717, 7757

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A260828, A260829, A260891, A385779.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 5, 6, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 5, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("1567"), 41))) # uses function/imports in A385776

A386130 Primes having only {1, 5, 6, 8} as digits.

Original entry on oeis.org

5, 11, 61, 151, 181, 661, 811, 881, 1151, 1181, 1511, 1811, 1861, 5581, 5651, 5851, 5861, 5881, 6151, 6551, 6581, 6661, 8111, 8161, 8581, 8681, 8861, 11161, 11551, 11681, 15161, 15511, 15551, 15581, 15661, 15881, 16111, 16561, 16651, 16661, 16811, 18181, 18661

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A385779, A385780, A385782.

Cf. A000040, A030430, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 5, 6, 8]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 6, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 5, 6, 8]) \\ uses function in A385776

print(list(islice(primes_with("1568"), 41))) # uses function/imports in A385776

A386131 Primes having only {1, 5, 6, 9} as digits.

Original entry on oeis.org

5, 11, 19, 59, 61, 151, 191, 199, 569, 599, 619, 659, 661, 691, 911, 919, 991, 1151, 1511, 1559, 1619, 1669, 1699, 1951, 1999, 5119, 5519, 5569, 5591, 5651, 5659, 5669, 6151, 6199, 6551, 6569, 6599, 6619, 6659, 6661, 6691, 6911, 6959, 6961, 6991, 9151, 9161, 9199

Offset: 1

Jason Bard, Jul 17 2025

Supersequence of A363023, A385779, A385781, A385797.

Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [1, 5, 6, 9]];

Flatten[Table[Select[FromDigits /@ Tuples[{1, 5, 6, 9}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [1, 5, 6, 9]) \\ uses function in A385776

print(list(islice(primes_with("1569"), 41))) # uses function/imports in A385776

cp's OEIS Frontend

A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + u*x^2 + v*x + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.

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A386031 Primes having only {0, 1, 5, 6} as digits.

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A386095 Primes having only {1, 2, 5, 6} as digits.

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A386110 Primes having only {1, 3, 5, 6} as digits.

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A386119 Primes having only {1, 4, 5, 6} as digits.

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A386129 Primes having only {1, 5, 6, 7} as digits.

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A386130 Primes having only {1, 5, 6, 8} as digits.

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A386131 Primes having only {1, 5, 6, 9} as digits.

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A385880 Values of u in triples (u, v, w) such that the polynomial x^3 + ux^2 + vx + w has 3 distinct negative integer zeros; the triples are ordered by the inequality u < v.