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.

A316488 Squares whose arithmetic mean of digits is 8 (i.e., the sum of digits is 8 times the number of digits).

Original entry on oeis.org

97969, 88998998929, 97888999968769, 38999699989995889, 79949788888999969, 98987998979757889, 99497897999899876, 498999778899898896, 597998978979699969, 799778987996998689, 896899597989995889, 899984989899599769, 979978999994798769, 989999999787828969
Offset: 1

Views

Author

Jon E. Schoenfield, Jul 04 2018

Keywords

Comments

Each term's number of digits is in A174438 (Numbers that are congruent to {0, 2, 5, 8} mod 9). For every positive term k in A174438, it appears that this sequence contains at least one k-digit term with the exception of k=2, k=8, and k=9. (See A316480.)

Examples

			313^2 = 97969, a 5-digit number whose digit sum is 9+7+9+6+9 = 40 = 8*5, so 97969 is a term.
9949823114^2 = 98998979999888656996, a 20-digit number whose digit sum is 9+8+9+9+8+9+7+9+9+9+9+8+8+8+6+5+6+9+9+6 = 160 = 8*20, so 98998979999888656996 is a term.
		

Crossrefs

Intersection of A000290 and A061425. - Michel Marcus, Jul 06 2018

A316482 Squares whose arithmetic mean of digits is 2 (i.e., the sum of digits is twice the number of digits).

Original entry on oeis.org

21025, 23104, 32041, 36100, 63001, 10125124, 10176100, 10233601, 10530025, 10824100, 11122225, 11303044, 11424400, 12040900, 12103441, 12222016, 12602500, 13315201, 13322500, 14055001, 14600041, 16008001, 16080100, 16810000, 20205025, 20214016, 20611600
Offset: 1

Views

Author

Jon E. Schoenfield, Jul 04 2018

Keywords

Comments

Each term's number of digits is in A174438 (Numbers that are congruent to {0, 2, 5, 8} mod 9). For every positive term k in A174438, this sequence contains at least one k-digit term, with the exception of k=2. (See A316480.)

Examples

			145^2 = 21025, a 5-digit number whose digit sum is 2+1+0+2+5 = 10 = 2*5, so 21025 is a term.
		

Crossrefs

Intersection of A000290 and A061385. - Michel Marcus, Jul 06 2018

A316485 Squares whose arithmetic mean of digits is 5 (i.e., the sum of digits is 5 times the number of digits).

Original entry on oeis.org

64, 12769, 14884, 24649, 24964, 27556, 30976, 33856, 37249, 37636, 44944, 48841, 56644, 65536, 66049, 70756, 75076, 75625, 80089, 80656, 85264, 96721, 10778089, 10982596, 11464996, 11498881, 11648569, 11957764, 11992369, 12369289, 12559936, 12687844, 12909649
Offset: 1

Views

Author

Jon E. Schoenfield, Jul 04 2018

Keywords

Comments

Each term's number of digits is in A174438 (Numbers that are congruent to {0, 2, 5, 8} mod 9). For every positive term k in A174438, this sequence contains at least one k-digit term. (See A316480.)

Examples

			8^2 = 64, a 2-digit number whose digit sum is 6+4 = 10 = 5*2, so 64 is a term.
3283^2 = 10778089, an 8-digit number whose digit sum is 1+0+7+7+8+0+8+9 = 40 = 5*8, so 10778089 is a term.
		

Crossrefs

Intersection of A000290 and A061388. - Michel Marcus, Jul 06 2018

Programs

  • Mathematica
    Select[Range[4000]^2,Mean[IntegerDigits[#]]==5&] (* Harvey P. Dale, Sep 10 2022 *)
Showing 1-3 of 3 results.