A087593 -id:A087593 - cp's OEIS frontend

A087595 Smallest n-digit member of A087593. Define dd(k) = the number formed by concatenating the absolute difference of successive digits of k. Sequence contains smallest n-digit prime p such that dd(p) is also prime.

13, 101, 1009, 10009, 100363, 1000003, 10000141, 100000543, 1000000007, 10000000589, 100000000447, 1000000000063, 10000000000609, 100000000000721, 1000000000000843, 10000000000002547, 100000000000000609

Offset: 2

Amarnath Murthy, Sep 18 2003

Conjecture: Sequence is infinite.

			a(5) = 10009 and dd(10009) = 1009 is a prime.

Cf. A087593, A087594, A087596.

More terms from David Wasserman, Jun 15 2005

A087596 Largest n-digit member of A087593. Define dd(k) = the number formed by concatenating the absolute difference of successive digits of k. Sequence contains largest n-digit prime p such that dd(p) is also prime.

Original entry on oeis.org

97, 997, 9967, 99989, 999907, 9999907, 99999989, 999999607, 9999999967, 99999999947, 999999999989, 9999999999701, 99999999999923, 999999999999989, 9999999999999887, 99999999999999997, 999999999999999989

Offset: 2

Amarnath Murthy, Sep 18 2003

Conjecture: Sequence is infinite.

			a(5) = 99989 and dd(99989) = 0011 = 11 is a prime.

Cf. A087593, A087594, A087595.

npr[n_]:=Module[{pr=NextPrime[10^n,-1]},While[!PrimeQ[FromDigits[Abs[ Differences[ IntegerDigits[pr]]]]],pr=NextPrime[pr,-1]];pr]; Array[ npr,20,2] (* Harvey P. Dale, Mar 06 2012 *)

More terms from David Wasserman, Jun 15 2005

A087594 Define dd(n) = the number formed by concatenating the absolute difference of successive digits. Sequence contains primes p such that dd(p)=q is a prime, dd(q) is also a prime = r and so on until a single-digit prime (2,3,5,7) arises. (Primes in which the number formed by successive digit differences are primes at every step until a single-digit prime is obtained.).

Original entry on oeis.org

13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 103, 113, 163, 227, 229, 331, 347, 367, 401, 449, 487, 503, 521, 523, 541, 547, 557, 563, 569, 587, 601, 661, 709, 743, 769, 821, 823, 881, 883, 907, 941, 947, 967, 997, 1063, 1069, 1103, 1163, 1481, 1609, 1621, 1663

Offset: 0

Amarnath Murthy, Sep 18 2003

Conjecture: Sequence is infinite. Subsidiary sequence: number of n-digit members.

			29 is a member as absolute(2-9) = 7 is a prime.
347 is a member as dd(347) = 13, dd(13) = 2.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A087593, A087595.

adsd[n_]:=FromDigits[Abs/@Differences[IntegerDigits[n]]]; Select[Prime[ Range[ 300]], And@@PrimeQ[NestWhileList[adsd,adsd[#],IntegerLength[#]>1&]]&] (* Harvey P. Dale, Mar 16 2013 *)

More terms from David Wasserman, Jun 15 2005

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

A087592 Primes whose successive differences are increasing power of 2: a(1) = 2, a(n+1) = a(n) + 2^k; a(n+1) prime, k minimal and greater than the index for the previous term.

Original entry on oeis.org

2, 3, 5, 13, 29, 61, 317, 829, 1073742653

Offset: 1

Amarnath Murthy, Sep 18 2003

nonn

Next term a(9) has 292 digits and is too large to include.

Cf. A033875, A087593.

Corrected and extended by Ray Chandler, Sep 25 2003

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)]);

cp's OEIS Frontend

A087595 Smallest n-digit member of A087593. Define dd(k) = the number formed by concatenating the absolute difference of successive digits of k. Sequence contains smallest n-digit prime p such that dd(p) is also prime.

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A087596 Largest n-digit member of A087593. Define dd(k) = the number formed by concatenating the absolute difference of successive digits of k. Sequence contains largest n-digit prime p such that dd(p) is also prime.

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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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Maple

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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A087592 Primes whose successive differences are increasing power of 2: a(1) = 2, a(n+1) = a(n) + 2^k; a(n+1) prime, k minimal and greater than the index for the previous term.

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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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Author

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Programs

Maple