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 1-4 of 4 results.

A321266 Smallest positive number for which the square cannot be written as sum of distinct squares of any subset of previous terms.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 64, 68, 96, 128, 136, 192, 256, 272, 384, 512, 544, 768, 1024, 1088, 1536, 2048, 2176, 3072, 4096, 4352, 6144, 8192, 8704, 12288, 16384, 17408, 24576, 32768, 34816, 49152, 65536, 69632, 98304, 131072, 139264
Offset: 1

Views

Author

Bert Dobbelaere, Nov 01 2018

Keywords

Comments

a(n)^2 = A226076(n) forms a sum-free sequence.

Examples

			0^2 = 0 (sum of squares of the empty set).
1^2 cannot be written as sum of squares of the empty set, so a(1)=1.
Suppose we determined all terms up to a(7)=12:
13^2 = 12^2 + 4^2 + 3^2,
14^2 = 12^2 + 6^2 + 4^2,
15^2 = 12^2 + 8^2 + 4^2 + 1^2.
16^2 cannot be written as sum of squares of distinct smaller terms, hence a(8)=16.

Links

Crossrefs

Square root of A226076.
Other powers: A321290 (3), A321291 (4), A321292 (5), A321293 (6).

Programs

  • Python
    def findSum(nopt, tgt, a, smax, pwr):
    if nopt==0:
        return [] if tgt==0 else None
    if tgt<0 or tgt>smax[nopt-1]:
        return None
    rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
    if rv!=None:
        rv.append(a[nopt-1])
    else:
        rv=findSum(nopt-1,tgt, a, smax, pwr)
    return rv
def A321266(n):
    POWER=2 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)

Formula

a(n) = 2 * a(n-3) for n > 9 (conjectured).

A321291 Smallest positive number for which the 4th power cannot be written as sum of 4th powers of any subset of previous terms.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 32, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 64, 68, 72, 76, 80, 84, 88, 92, 96, 104, 108, 112, 128, 136, 144, 152, 160, 168, 176, 184, 192, 208, 216, 224, 256
Offset: 1

Views

Author

Bert Dobbelaere, Nov 02 2018

Keywords

Comments

a(n)^4 forms a sum-free sequence.
It is noteworthy that the terms of this sequence increase slower than those of similar sequences for smaller (A321266, A321290) but also larger powers (A321292, A321293).

Examples

			The smallest number > 0 that is not in the sequence is 15, because
    15^4 = 4^4 + 6^4 + 8^4 + 9^4 + 14^4.

Links

Crossrefs

Other powers: A321266 (2), A321290 (3), A321292 (5), A321293 (6).

Programs

  • Python
    def findSum(nopt, tgt, a, smax, pwr):
    if nopt==0:
        return [] if tgt==0 else None
    if tgt<0 or tgt>smax[nopt-1]:
        return None
    rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
    if rv!=None:
        rv.append(a[nopt-1])
    else:
        rv=findSum(nopt-1, tgt, a, smax, pwr)
    return rv
def A321291(n):
    POWER=4 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)

Formula

a(n) = 2 * a(n-12) for n > 25 (conjectured).

A321292 Smallest positive number for which the 5th power cannot be written as sum of distinct 5th powers of any subset of previous terms.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 30, 37, 43, 44, 55, 57, 64, 77, 82, 90, 97, 112, 116, 119, 154, 156, 178, 202, 227, 269, 309, 335, 371, 397, 442, 516, 604, 643, 722, 774, 815, 1000, 1115, 1308, 1503
Offset: 1

Views

Author

Bert Dobbelaere, Nov 02 2018

Keywords

Comments

a(n)^5 forms a sum-free sequence.

Examples

			The smallest number > 0 that is not in the sequence is 12, because
12^5 = 4^5 + 5^5 + 6^5 + 7^5 + 9^5 + 11^5.

Links

Crossrefs

Other powers: A321266 (2), A321290 (3), A321291 (4), A321293 (6).

Programs

  • Python
    def findSum(nopt, tgt, a, smax, pwr):
    if nopt==0:
        return [] if tgt==0 else None
    if tgt<0 or tgt>smax[nopt-1]:
        return None
    rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
    if rv!=None:
        rv.append(a[nopt-1])
    else:
        rv=findSum(nopt-1, tgt, a, smax, pwr)
    return rv
def A321292(n):
    POWER=5 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)

A321293 Smallest positive number for which the 6th power cannot be written as sum of distinct 6th powers of any subset of previous terms.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 42, 43, 51, 57, 60, 61, 71, 74, 88, 91, 99, 112, 116, 117, 132, 152, 153, 176, 203, 228, 244, 256, 281, 293, 345, 392, 439, 441, 529, 594, 627
Offset: 1

Views

Author

Bert Dobbelaere, Nov 02 2018

Keywords

Comments

a(n)^6 forms a sum-free sequence.

Examples

			The smallest number > 0 that is not in the sequence is 25, because 25^6 = 1^6 + 2^6 + 3^6 + 5^6 + 6^6 + 7^6 + 8^6 + 9^6 + 10^6 + 12^6 + 13^6 + 15^6 + 16^6 + 17^6 + 18^6 + 23^6.

Links

Crossrefs

Other powers: A321266 (2), A321290 (3), A321291 (4), A321292 (5).

Programs

  • Python
    def findSum(nopt, tgt, a, smax, pwr):
    if nopt==0:
        return [] if tgt==0 else None
    if tgt<0 or tgt>smax[nopt-1]:
        return None
    rv=findSum(nopt-1, tgt - a[nopt-1]**pwr, a, smax, pwr)
    if rv!=None:
        rv.append(a[nopt-1])
    else:
        rv=findSum(nopt-1, tgt, a, smax, pwr)
    return rv
def A321293(n):
    POWER=6 ; x=0 ; a=[] ; smax=[] ; sumpwr=0
    while len(a)
Showing 1-4 of 4 results.

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