A040997 -id:A040997 - cp's OEIS frontend

A115260 Prime numbers in the sequence of the absolute difference of the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

2, 3, 5, 7, 2, 7, 2, 3, 3, 2, 5, 2, 5, 2, 2, 3, 5, 7, 3, 3, 2, 2, 3, 3, 7, 5, 2, 3, 7, 2, 2, 5, 2, 5, 3, 3, 5, 7, 7, 5, 2, 5, 13, 3, 2, 3, 5, 3, 2, 7, 2, 5, 5, 7, 13, 3, 5, 2, 2, 7, 13, 3, 2, 3, 5, 17, 7, 13, 5, 3, 7, 17, 13, 7, 3, 7, 7, 2, 3, 5, 5, 2, 2, 7, 3, 3, 7, 2, 3, 7, 2, 3, 7, 2, 5, 5, 3, 2, 7, 3, 5, 7

Offset: 1

Giorgio Balzarotti, Paolo P. Lava, Jan 20 2006

Primes in the sequence A115259.

			a(37) = 3 because 37th prime = 157, (7+1) - 5 = 3, 3 is prime.

Cf. A040997, A005017, A063792, A087593, A042939, A041000, A040164, A115259, A115261.

select(isprime,[seq(abs(sum(convert(ithprime(a),base,10)[2*i],i=1..nops(convert (ithprime(a),base,10))/2)-sum(convert(ithprime(a),base,10)[2*i+1],i=0..(nops (convert(ithprime(a),base,10))-1)/2)),a=1..N)]);

A193772 Nonnegative integers whose digital difference is 0.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 202, 211, 220, 303, 312, 321, 330, 404, 413, 422, 431, 440, 505, 514, 523, 532, 541, 550, 606, 615, 624, 633, 642, 651, 660, 707, 716, 725, 734, 743, 752, 761, 770, 808, 817, 826, 835, 844, 853, 862, 871, 880

Offset: 1

Dario Piazzalunga, Jan 02 2013

The subsequence of multiples of 11 begins: 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 220, 330, 440...

The subsequence of primes begins: 11, 101, 211, 431, 523, 541, 743, 761, 853, ... (see A156307).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A040997, A007953, A156307.

V:= proc(n,s) # n-digits numbers with sum of digits s
     option remember; local i,k;
     `union`(seq(seq(map(t -> i*10^(n-1) + t, procname(k,s-i)),k=1..n-1),i=1..min(s,9)))
end proc:
for s from 0 to 9 do V(1,s) := {s} od:
f:= proc(n) local s,k;
   `union`(seq(seq(map(t -> s*10^(n-1) + t, V(k,s)), k=1..n-1),s=1..9))
end proc:
sort(convert(`union`(seq(f(d),d=1..4)),list)); # Robert Israel, Nov 14 2024

fQ[n_] := Module[{d = IntegerDigits[n]}, d[[1]] == Total[Rest[d]]]; Select[Range[0, 1000], fQ] (* T. D. Noe, Jan 02 2013 *)

If decimal expansion of n is x1 x2 ... xk then x1 - x2 - ... - xk = 0.

Definition edited by Michel Marcus, Oct 26 2014

A241494 Pyramid Top Numbers: write the decimal digits of 'n' (a nonnegative integer) and take successive absolute differences ("pyramidalization"). The number at the top of the pyramid is 'a(n)'.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5

Offset: 0

Filipi R. de Oliveira, Apr 24 2014

Through the so-called "pyramidalization" process (see A227876), a given nonnegative integer is expanded into its digits and transformed into a pyramid of successive absolute differences between digits. The present sequence is built only with the top number 'a(n)' generated from its correspondent nonnegative integer 'n'.

			If n=1735, a(n)=0:
______0 ------>a(n)
____2_:_2
__6_:_4_:_2
1_:_7_:_3_:_5

Filipi R. de Oliveira, Table of n, a(n) for n = 0..9999

Cf. A227876 for the pyramidalization process.

Cf. A076313 - its first 100 terms have the same absolute value, diverging afterwards; cf. A225693 and A055017 (A040997) for the same reason.

a(n)=my(d=Vecsmall(digits(n))); forstep(k=#d-1,1,-1, for(j=1,k, d[j]=abs(d[j]-d[j+1]))); d[1] \\ Charles R Greathouse IV, Apr 24 2025

a(n)=n, if 0<=n<=9.

a(n)=|mod(n;10)-floor(n/10)|, if 10<=n<=99.

A274580 Digital difference of n: the most significant decimal digit of n minus the sum of the other digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Felix Fröhlich, Jun 29 2016

If A007953(n) is seen as giving the resulting sum when inserting "+" signs between the digits of n, then a(n) gives the resulting difference when inserting "-" signs between the digits of n.
a(n) = 0 if and only if n is in A193772.
Signed version of A040997.
First differs from A225693 at n = 101.
abs(a(n)) first differs from abs(A055017(n)) at n = 102.

			a(13) = 1 - 3 = -2.
a(74) = 7 - 4 = 3.
a(211) = 2 - 1 - 1 = 0.

Cf. A007953, A007954.

Table[Fold[#1 - #2 &, IntegerDigits@ n], {n, 76}] (* Michael De Vlieger, Jun 30 2016 *)
Table[-Differences[(Total/@TakeDrop[IntegerDigits[n],1])],{n,100}]//Flatten (* Harvey P. Dale, Dec 27 2022 *)

diffdigits(n) = my(d=digits(n), dd=d[1]); for(k=2, #d, dd=dd-d[k]); dd
a(n) = diffdigits(n)

a(n) = A000030(n) - A007953(A217657(n)).

cp's OEIS Frontend

A115260 Prime numbers in the sequence of the absolute difference of the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

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A193772 Nonnegative integers whose digital difference is 0.

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A241494 Pyramid Top Numbers: write the decimal digits of 'n' (a nonnegative integer) and take successive absolute differences ("pyramidalization"). The number at the top of the pyramid is 'a(n)'.

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A274580 Digital difference of n: the most significant decimal digit of n minus the sum of the other digits.

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