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 1-5 of 5 results.

A328619 Inverse permutation to A328618.

Original entry on oeis.org

1, 2, 9, 4, 125, 18, 2401, 8, 3, 250, 1771561, 36, 62748517, 4802, 1125, 16, 118587876497, 6, 6131066257801, 500, 21609, 3543122, 21914624432020321, 72, 5, 125497034, 27, 9604, 8629188747598184440949, 2250, 727423121747185263828481, 32, 15944049, 237175752994, 300125, 12, 624931990990842127748277129373, 12262132515602, 564736653, 1000
Offset: 1

Views

Author

Antti Karttunen, Oct 23 2019

Keywords

Links

Crossrefs

Cf. A328617, A328618.

Programs

  • PARI
    A328619(n) = { my(f = factor(n), m, q); for(k=1, #f~, q = (f[k, 2]\f[k, 1]); m = (f[k, 2]%f[k, 1]); if(m&&(f[k,1]!=2), f[k, 2] = q*f[k, 1] + lift(Mod(m,f[k, 1])/2))); factorback(f); };

A328622 In primorial base representation of n, multiply by 2 all other digits except the least significant, and reduce each such product modulo prime(k) (to get the new digit), where k > 1 is the position of the digit, then convert back to decimal.

Original entry on oeis.org

0, 1, 4, 5, 2, 3, 12, 13, 16, 17, 14, 15, 24, 25, 28, 29, 26, 27, 6, 7, 10, 11, 8, 9, 18, 19, 22, 23, 20, 21, 60, 61, 64, 65, 62, 63, 72, 73, 76, 77, 74, 75, 84, 85, 88, 89, 86, 87, 66, 67, 70, 71, 68, 69, 78, 79, 82, 83, 80, 81, 120, 121, 124, 125, 122, 123, 132, 133, 136, 137, 134, 135, 144, 145, 148, 149, 146, 147, 126, 127, 130, 131
Offset: 0

Views

Author

Antti Karttunen, Oct 23 2019

Keywords

Examples

			In primorial base (A049345) 199 is written as "6301" because 6*A002110(3) + 3*A002110(2) + 0*A002110(1) + 1*A002110(0) = 6*30 + 3*6 + 0*2 + 1*1 = 199. Multiplying each digit except the least significant by 2, and then reducing them modulo the corresponding prime leaves us with 2*6 mod 7, 2*3 mod 5, 2*0 mod 3, (with the least significant 1 staying the same), so we get "5101", which is the primorial base expansion of 157, thus a(199) = 157.
For 157, the new "doubled and reduced" expansion is 2*5 mod 7, 2*1 mod 5, 2*0 mod 3 and the trailing 1 stays intact, so we get "3201", which is the primorial base expansion of 103, thus a(157) = 103.

Links

Crossrefs

Cf. A328623 (inverse), and also A289234.
Cf. A002110, A049345, A276085, A276086, A328618.

Programs

  • PARI
    A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328618(n) = { my(f = factor(n), m, q); for(k=1, #f~, q = (f[k, 2]\f[k, 1]); m = (f[k, 2]%f[k, 1]); if(m&&(f[k,1]!=2), f[k, 2] = q*f[k, 1] + ((2*f[k, 2])%f[k, 1]))); factorback(f); };
A328622(n) = A276085(A328618(A276086(n)));

Formula

a(n) = A276085(A328618(A276086(n))).

A346102 a(n) = A276086(A328622(n)).

Original entry on oeis.org

1, 2, 9, 18, 3, 6, 25, 50, 225, 450, 75, 150, 625, 1250, 5625, 11250, 1875, 3750, 5, 10, 45, 90, 15, 30, 125, 250, 1125, 2250, 375, 750, 49, 98, 441, 882, 147, 294, 1225, 2450, 11025, 22050, 3675, 7350, 30625, 61250, 275625, 551250, 91875, 183750, 245, 490, 2205, 4410, 735, 1470, 6125, 12250, 55125, 110250, 18375, 36750, 2401
Offset: 0

Views

Author

Antti Karttunen, Jul 11 2021

Keywords

Links

Crossrefs

Cf. A002110, A276085, A276086, A328618, A328622, A346233, A346252.

Programs

  • PARI
    A346102(n) = { my(m=1, p=2); while(n, m *= (p^((((p%2)+1)*n)%p)); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A276086(A328622(n)).
A342001(a(n)) = A346252(n).

A328617 Multiplicative with a(p^e) = p^e, if e = 0 mod p, otherwise a(p^e) = p^((p*floor(e/p)) + A124223(A000720(p),e mod p)).

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, 125, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 2401, 250, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 375, 76, 77, 78, 79, 80, 81
Offset: 1

Views

Author

Antti Karttunen, Oct 23 2019

Keywords

Links

Crossrefs

Cf. A124223, A327938, A289234.
Cf. also A328618, A328619.

Programs

  • PARI
    A328617(n) = { my(f = factor(n), m, q); for(k=1, #f~, q = (f[k, 2]\f[k, 1]); m = (f[k, 2]%f[k, 1]); if(m, f[k, 2] = q*f[k, 1] + lift(1/Mod(m,f[k, 1])))); factorback(f); };

Formula

For all n >= 0, A276085(a(A276086(n))) = A289234(n).

A328621 Multiplicative with a(p^e) = p^(2e mod p).

Original entry on oeis.org

1, 1, 9, 1, 25, 9, 49, 1, 3, 25, 121, 9, 169, 49, 225, 1, 289, 3, 361, 25, 441, 121, 529, 9, 625, 169, 1, 49, 841, 225, 961, 1, 1089, 289, 1225, 3, 1369, 361, 1521, 25, 1681, 441, 1849, 121, 75, 529, 2209, 9, 2401, 625, 2601, 169, 2809, 1, 3025, 49, 3249, 841, 3481, 225, 3721, 961, 147, 1, 4225, 1089, 4489, 289, 4761, 1225, 5041, 3, 5329
Offset: 1

Views

Author

Antti Karttunen, Oct 23 2019

Keywords

Links

Crossrefs

Cf. A011262, A327938, A328618 (a bijective variant).

Programs

  • PARI
    A328621(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = ((2*f[k,2])%f[k,1])); factorback(f); };
Showing 1-5 of 5 results.

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