cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A036057 Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results).

Original entry on oeis.org

25, 121, 125, 126, 127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024, 1206, 1255, 1260, 1285, 1296, 1395, 1435, 1503, 1530, 1792, 1827, 2048, 2187, 2349, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 2592, 2737, 2916, 3125, 3159
Offset: 1

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Author

Erich Friedman

Keywords

Comments

Mitchell's and Wilson's lists both lack two terms, 16387 = (1-6/8)^(-7)+3 and 41665 = 641*65. - Giovanni Resta, Dec 14 2013
Primes in this sequence are listed in A112419. See also the subsequence A080035 of "orderly" terms, and its subset A156954. - M. F. Hasler, Jan 04 2015

Examples

			E.g., 153=51*3, 736=3^6+7. Not 26 = 2 6 (concatenated), that's trivial.

Links

Crossrefs

Cf. A080035, A156954, A046469.

Formula

a(n) ~ n, see Brand. - Charles R Greathouse IV, Jun 04 2013

Extensions

Edited by Michel Marcus and M. F. Hasler, Jan 04 2015

A080035 "Orderly" Friedman numbers (or "good" or "nice" Friedman numbers): Friedman numbers (A036057) where the construction digits are used in the proper order.

Original entry on oeis.org

127, 343, 736, 1285, 2187, 2502, 2592, 2737, 3125, 3685, 3864, 3972, 4096, 6455, 11264, 11664, 12850, 13825, 14641, 15552, 15585, 15612, 15613, 15617, 15618, 15621, 15622, 15623, 15624, 15626, 15632, 15633, 15642, 15645, 15655, 15656
Offset: 1

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Author

David Rattner (david_rattner(AT)prusec.com), Mar 14 2003

Keywords

Comments

Primes in this sequence are listed in A252483. The subsequence A156954 is a simpler variant where no parentheses, unary operations (negation) nor concatenation is allowed. - M. F. Hasler, Jan 07 2015

Examples

			127 = -1 + 2^7, 343 = (3 + 4) ^ 3, 736 = 7 + 3^6, etc.
The 4th "orderly" Friedman number is 1285 = (1 + 2^8) * 5.

References

  • Credit goes to Mike Reid (Brown University) and Eric Friedman (Stetson University).
  • Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254. See page 251.

Links

Crossrefs

Cf. A036057.

Extensions

More terms from Alonso del Arte, Aug 25 2004
Edited by M. F. Hasler, Jan 07 2015

A386936 Numbers that can be represented using their digits in the order of appearance, the operations +, -, *, /, ^, and any parentheses.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 343, 736, 1285, 2187, 2592, 2737, 3125, 3685, 3972, 4096, 6455, 11664, 14641, 15552, 15585, 15617, 15618, 15622, 15624, 15626, 15632, 15645, 15655, 15656, 15662, 15667, 15698, 16377, 16384, 17536, 19683, 23328, 24576, 27639
Offset: 1

Views

Author

Anuraag Pasula and Walter Robinson, Aug 09 2025

Keywords

Comments

Each digit is its own operand (no concatenation of digits).
Real and imaginary intermediate values are allowed as long as the final value of the expression is an integer.
Unary minus is not allowed, otherwise we would have 127 = -1 + 2^7. - Sean A. Irvine, Aug 31 2025

Examples

			343 = (3+4)^3.
2737 = (2*7)^3-7.
46688 = (4 + 6^6/8)*8.

Links

Crossrefs

Cf. A036057, A046469, A080035, A156954, A362769.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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