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.

A381034 Numbers that have a digit > 1 in their primorial base expansion, and that are multiples of the corresponding radix prime of the least significant such digit.

Original entry on oeis.org

15, 20, 25, 45, 50, 55, 63, 75, 80, 85, 91, 98, 105, 110, 115, 126, 135, 140, 145, 165, 170, 175, 182, 189, 195, 200, 205, 225, 230, 235, 255, 260, 265, 273, 285, 290, 295, 301, 308, 315, 320, 325, 336, 345, 350, 355, 375, 380, 385, 392, 399, 405, 410, 415, 429, 435, 440, 445, 451, 465, 470, 475, 483, 495, 500, 505
Offset: 1

Views

Author

Antti Karttunen, Feb 17 2025

Keywords

Examples

			A049345(15) = 211, the least significant digit larger than one is 2, where the corresponding radix prime is 5, and 5 divides 15, therefore 15 is included.

Links

Crossrefs

Cf. A049345, A381032, A381033 (characteristic function), A381037 (subsequence).
Subsequence of the intersection A177711 and A381035.

Programs

A380527 Numbers k such that k is a multiple of A327860(k), where A327860 is the arithmetic derivative of the primorial base exp-function.

Original entry on oeis.org

1, 2, 6, 7, 8, 30, 36, 210, 2310, 2340, 2520, 2556, 30030, 30240, 32340, 510510, 510720, 540540, 9699690, 9699720, 9702000, 9729720, 10210200, 223092870, 223092900, 223093080, 223095180, 232792560, 6469693230, 6469693236, 6469693440, 6469695540, 6692786100
Offset: 1

Views

Author

Antti Karttunen, Feb 11 2025

Keywords

Comments

It is conjectured that only terms of A276156 occur here. If any term of A177711 is included, then it must be one of the terms of A381037.
a(34) > A143293(10).

Links

Crossrefs

Cf. A003415, A053669, A143293, A276086, A327860.
Subsequence of A381035. Conjectured to be a subsequence of A276156.
Subsequences: A002110, A328110.
Cf. also A177711, A351087, A381037.

Programs

  • PARI
    A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
is_A380527(n) = !(n%A327860(n));

A381037 Numbers with a digit > 1 in their primorial base expansion that are multiples of the corresponding radix primes of all such digits.

Original entry on oeis.org

15, 20, 25, 45, 50, 55, 63, 91, 98, 105, 126, 140, 175, 182, 189, 225, 230, 235, 255, 260, 265, 273, 301, 308, 315, 336, 350, 385, 392, 399, 429, 440, 451, 638, 660, 693, 770, 847, 1056, 1089, 1100, 1155, 1232, 1298, 1386, 1485, 1507, 1683, 1705, 1716, 1771, 1892, 2079, 2101, 2145, 2325, 2330, 2335, 2355, 2360, 2365
Offset: 1

Views

Author

Antti Karttunen, Feb 17 2025

Keywords

Comments

Numbers k such that A328572(k) > 1 and A007947(A328572(k)) divides k.

Examples

			For n=75, A049345(75) = 2211, with two digits > 1. Their corresponding radix primes are 5 and 7, but as 75 is a multiple of only 5 but not of 7, 75 is NOT included in this sequence.
For n = 105, A049345(105) = 3211, with two digits > 1. Their corresponding radix primes are 5 and 7 that both divide 105, therefore 105 is included.

Links

Crossrefs

Subsequence of A381034, thus subsequence of the intersection A177711 and A381035.
Cf. A003557, A007947, A049345, A276086, A328572, A381036 (characteristic function).
Cf. also A380527.

Programs

Showing 1-3 of 3 results.

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

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