A040164 -id:A040164 - cp's OEIS frontend

A042939 Absolute values between digits of primes.

2, 3, 5, 7, 0, 2, 6, 8, 1, 7, 2, 4, 3, 1, 3, 2, 4, 5, 1, 6, 4, 2, 5, 1, 2, 0, 2, 6, 8, 3, 8, 3, 9, 11, 12, 5, 11, 8, 12, 9, 15, 8, 9, 11, 15, 17, 0, 3, 7, 9, 4, 10, 3, 4, 10, 7, 13, 6, 12, 7, 9, 10, 4, 1, 1, 5, 1, 7, 8, 10, 5, 11, 10, 7, 13, 8, 14, 13, 3, 5, 6, 1, 0, 2, 8, 3, 9, 8, 3, 5, 9, 12, 11, 6

Offset: 1

Felice Russo

a(n) = absolute difference between the first digit of prime(n) and the sum of the other digits of prime(n). [Harvey P. Dale, Mar 11 2012]

James Spahlinger, Table of n, a(n) for n = 1..10000

Cf. A041000, A040164, A000040.

Cf. A007605.

a042939 = a040997 . a000040
-- Reinhard Zumkeller, Oct 10 2012

ddp[n_]:=Module[{idn=IntegerDigits[n]},Abs[First[idn]-Total[Rest[idn]]]]; ddp/@Prime[Range[100]] (* Harvey P. Dale, Mar 11 2012 *)

If decimal expansion of n-th prime is x1 x2 x3......xk then a(n)=|x1-x2-x3.......-xk|

a(n) = A040997(A000040(n)). - Reinhard Zumkeller, Oct 10 2012

A041000 If decimal expansion of n-th prime is x1 x2 ... xk, sort the xi into nonincreasing order, y1 y2 ... yk; then a(n) = |y1-y2-y3...-yk|.

Original entry on oeis.org

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

Offset: 1

Felice Russo

			a(397)=|9-7-3|=1.

Cf. A040164, A007953, A054055.

der[n_]:=Module[{c=Reverse[Sort[IntegerDigits[n]]]},Abs[First[c]-Total[Rest[c]]]]; der/@Prime[Range[110]] (* Harvey P. Dale, Aug 15 2012 *)

a(n) = |A007953(n)-2*A054055(n)|. [Charles R Greathouse IV, May 07 2011]

More terms from Michel ten Voorde

A115261 Prime numbers such that the absolute difference of the sum of their digits in odd positions and the sum of their digits in even positions is also a prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 101, 113, 137, 139, 151, 157, 163, 167, 173, 179, 191, 193, 211, 223, 227, 233, 251, 269, 277, 281, 283, 311, 313, 337, 359, 379, 383, 401, 409, 421, 431, 443, 467, 487, 541, 557, 563, 577, 599, 601, 607, 641

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Jan 20 2006

			1237 is in the sequence because it is prime and abs((7+2)-(3+1)) = 5 is prime

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A040997, A005017, A063792, A087593, A042939, A041000, A040164, A115259, A115260.

Df:=proc(N) j:=1; for n from 1 while j<=N do B:= convert(ithprime(n),base,10); ap:=-(sum(B[2*i],i=1..nops(B)/2)-sum(B[2*n+1],i=0..(nops(B)-1)/2)); if (isprime(abs(ap)) = true) then a[j]:=ithprime(n); j:=j+1; fi; od; end:

A115259 Difference between the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

Original entry on oeis.org

2, 3, 5, 7, 0, 2, 6, 8, 1, 7, -2, 4, -3, -1, 3, -2, 4, -5, 1, -6, -4, 2, -5, 1, -2, 2, 4, 8, 10, 3, 6, -1, 5, 7, 6, -3, 3, -2, 2, -3, 3, -6, -7, -5, -1, 1, 2, 3, 7, 9, 2, 8, -1, -2, 4, -1, 5, -4, 2, -5, -3, -4, 10, 3, 5, 9, 1, 7, 6, 8, 1, 7, 4, -1, 5, -2, 4, 1, 5, 13, 12, 3, 2, 4, 10, 3, 9, 6, -1, 1, 5, 6, 3, -4, 4, 8, 14, 4, 6, 2, 8, 7, 2, 8, -1, 5, 4, -1, 5, 7

Offset: 1

Giorgio Balzarotti and Paolo P. Lava, Jan 20 2006

Zero corresponds to the prime 11. It is easy to show that there is no other zero: if the difference of odd-even digits of a number is zero, the number is a multiple of 11, i.e., it is not a prime.

Positions are counted from the least to the most significant digit, so for prime 17 the odd digit is 7 and the even digit is 1. - Harvey P. Dale, Dec 15 2022

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

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

Cf. A040997, A055017, A063792, A087593, A042939, A041000, A040164, A115260, A115261.

A115259 := proc(n) A055017(ithprime(n)) ; end proc: # R. J. Mathar, Aug 26 2011

Table[Total[Take[Reverse[IntegerDigits[p]],{1,-1,2}]]-Total[Take[Reverse[IntegerDigits[p]],{2,-1,2}]],{p,Prime[Range[120]]}] (* Harvey P. Dale, Dec 15 2022 *)

a(n) = A055017(A000040(n)). - R. J. Mathar, Aug 26 2011

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.

Original entry on oeis.org

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)]);

A084686 Take n-th prime p(n), rewrite it with digits in decreasing order to get b(n), then a(n)=(b(n)-p(n))/9.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 6, 8, 1, 7, 0, 4, 0, 0, 3, 0, 4, 0, 1, 0, 0, 2, 0, 1, 0, 1, 23, 67, 89, 22, 66, 20, 66, 88, 88, 40, 66, 52, 66, 62, 88, 70, 80, 82, 86, 88, 0, 11, 55, 77, 11, 77, 20, 30, 55, 41, 77, 50, 55, 60, 61, 71, 47, 0, 2, 46, 0, 44, 44, 66, 20, 66, 44, 40, 66, 50, 66, 64, 1, 59, 58

Offset: 1

Zak Seidov, Jun 30 2003

			a(7)=6 because p(7)=17, b(n)=71 and (71-17)/9=6.

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

Cf. A040164, A085307.

f:= proc(n) local p,L,i;
  p:= ithprime(n);
  L:= sort(convert(p,base,10));
  (add(10^(i-1)*L[i],i=1..nops(L))-p)/9
end proc:
map(f, [$1..100]); # Robert Israel, Nov 26 2019

Table[ -Prime[n]-FromDigits[Sort[ -IntegerDigits[Prime[n]]]], {n, 1, 100}]

a(n) = A283001(A000040(n)). - Robert Israel, Nov 26 2019

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A042939 Absolute values between digits of primes.

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A041000 If decimal expansion of n-th prime is x1 x2 ... xk, sort the xi into nonincreasing order, y1 y2 ... yk; then a(n) = |y1-y2-y3...-yk|.

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A115261 Prime numbers such that the absolute difference of the sum of their digits in odd positions and the sum of their digits in even positions is also a prime.

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A115259 Difference between the sum of digits in odd positions and the sum of digits in even positions of prime numbers.

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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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A084686 Take n-th prime p(n), rewrite it with digits in decreasing order to get b(n), then a(n)=(b(n)-p(n))/9.

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