A085562 -id:A085562 - cp's OEIS frontend

A085563 Sum of the prime digits of n.

0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 2, 2, 4, 5, 2, 7, 2, 9, 2, 2, 3, 3, 5, 6, 3, 8, 3, 10, 3, 3, 0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 5, 5, 7, 8, 5, 10, 5, 12, 5, 5, 0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 7, 7, 9, 10, 7, 12, 7, 14, 7, 7, 0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 0, 2, 3

Offset: 1

Jason Earls, Jul 05 2003

			a(1234567)=17 because 2+3+5+7=17.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A007953, A085562.

Table[Total[Select[IntegerDigits[n],PrimeQ]],{n,110}] (* Harvey P. Dale, Aug 15 2020 *)

a(n) = vecsum(select(isprime, digits(n))); \\ Michel Marcus, Feb 06 2021

a(n)+A085562(n) = A007953(n). [R. J. Mathar, Aug 04 2008]

A341013 The cumulative sum of the prime digits so far in the sequence and the cumulative sum of the nonprime digits so far differ by n for all a(n) values.

Original entry on oeis.org

1, 3, 12, 16, 10, 34, 43, 56, 65, 78, 87, 100, 236, 258, 263, 285, 304, 326, 340, 359, 362, 395, 403, 430, 447, 474, 506, 528, 539, 560, 582, 593, 605, 623, 632, 650, 708, 744, 780, 807, 825, 852, 870, 935, 953, 1000, 1112, 1121, 1145, 1154, 1167, 1176

Offset: 1

Carole Dubois and Eric Angelini, Feb 02 2021

The prime digits are 2, 3, 5 and 7; the nonprime digits are 0, 1, 4, 6, 8 and 9.

This is the lexicographically earliest sequence of distinct integers > 0 having this property.

			Say that the current sequence is S, the cumulative sum at any moment of the prime digits of S is P, the cumulative sum at any moment of the nonprime digits of S is N and the absolute difference |P-N| is D. We would then have:
S =  1, 3, 12, 16, 10, 34, 43, 56, 65, 78, 87, 100,...
P =  0  3   5   5   5   8  11  16  21  28  35   35
N =  1  1   2   9  10  14  18  24  30  38  46   47
D =  1  2   3   4   5   6   7   8   9  10  11   12 <-- this is = n

Carole Dubois, Table of n, a(n) for n = 1..5000

Cf. A085562, A085563.

Cf. A341012 (the cumulative sums of even vs odd digits differ by n).

A341161 The sum of the prime digits of m and the sum of the nonprime digits of m differ by n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 119, 48, 49, 68, 69, 88, 89, 99, 199, 488, 489, 499, 689, 699, 889, 899, 999, 1999, 4889, 4899, 4999, 6899, 6999, 8899, 8999, 9999, 19999, 48899, 48999, 49999, 68999, 69999, 88999, 89999, 99999, 199999, 488999

Offset: 1

Carole Dubois and Eric Angelini, Feb 06 2021

This is the lexicographically earliest sequence of distinct terms > 0 with this property.

The nonprime digits are 0, 1, 4, 6, 8 and 9; the prime digits are 2, 3, 5 and 7. After a(7) = 7 no more terms will show a prime digit.

			The sequence:     1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 119, 48,...
Sum of prime dig. 0  2  3  0  5  0  7  0  0   0    0   0
Sum of nonprimes  1  0  0  4  0  6  0  8  9  10   11  12
Difference (= n)  1  2  3  4  5  6  7  8  9  10   11  12

Carole Dubois, Table of n, a(n) for n = 1..74

Cf. A085562, A085563, A341011.

cp's OEIS Frontend

A085563 Sum of the prime digits of n.

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A341013 The cumulative sum of the prime digits so far in the sequence and the cumulative sum of the nonprime digits so far differ by n for all a(n) values.

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A341161 The sum of the prime digits of m and the sum of the nonprime digits of m differ by n.

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