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.

A280915 Primes where difference between largest digit and all other digits is a positive square.

Original entry on oeis.org

11, 23, 37, 43, 59, 67, 73, 89, 101, 113, 127, 131, 149, 157, 167, 179, 197, 211, 239, 241, 257, 263, 269, 271, 293, 307, 311, 337, 347, 359, 373, 419, 421, 431, 449, 461, 491, 509, 523, 541, 571, 593, 607, 617, 641, 719, 733, 743, 751, 761, 809, 853, 941, 953, 971, 1013, 1021, 1031
Offset: 1

Views

Author

Osama Abuajamieh, Jan 10 2017

Keywords

Comments

If the largest digit L (say) is repeated, the criterion is that that L - (sum of all digits except for one copy of L) is a square.

Examples

			Prime 1153 is in a(n) since 5-3-1-1=0. Zero is square.
Prime 1163 is in a(n) since 6-3-1-1=1. One is square.
Prime 1171 is in a(n) since 7-1-1-1=4. Four is square.

Links

Crossrefs

This sequence is a parent sequence of A156753.

Programs

  • Mathematica
    Select[Prime@ Range@ 175, IntegerQ@ Sqrt@ Fold[#1 - #2 &, Max@ #, Rest@ #] &@ Reverse@ Sort@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)
  • PARI
    is(n)=my(d=digits(n)); issquare(2*vecmax(d)-vecsum(d)) && isprime(n) \\ Charles R Greathouse IV, Feb 05 2017

A280993 Primes such that the absolute value of the difference between the largest digit and the sum of all the other digits is a cube.

Original entry on oeis.org

11, 19, 23, 43, 67, 89, 101, 109, 113, 131, 157, 167, 179, 197, 199, 211, 223, 241, 257, 263, 269, 311, 313, 331, 337, 347, 353, 359, 373, 379, 397, 421, 431, 449, 461, 463, 523, 541, 571, 593, 607, 617, 641, 643, 661, 683, 719, 733, 739, 743
Offset: 1

Views

Author

Osama Abuajamieh, Jan 14 2017

Keywords

Comments

If the largest digit L (say) is repeated, the criterion is that |L - (sum of all digits except for one copy of L)| is a cube.

Examples

			The prime 2731 is a term, because 7-2-3-1 = 1 is a cube.
The prime 13 is not in the sequence, as 3-1 = 2, and 2 is not a cube.
The prime 313 is a term because |3 - (1+3)| = 1 is a cube.

Links

Crossrefs

A156753 and A156979 are subsequences.

Programs

  • Mathematica
    Select[Prime[Range[150]],IntegerQ[Surd[Abs[Max[IntegerDigits[#]]-Total[ Most[ Sort[IntegerDigits[#]]]]],3]]&] (* Harvey P. Dale, Dec 31 2021 *)
  • PARI
    listA280993(k, {k0=5})={my(H=List(), y); forprime(z=prime(k0), prime(k), y=digits(z); if(ispower(abs(vecsum(y)-2*vecmax(y)),3), listput(H, z))); return(vector(#H, i, H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017

A281170 Primes p whose decimal representation satisfy: abs(digsum(p)-2*L(p)) = 8, being L(p) the largest decimal digit in p.

Original entry on oeis.org

19, 109, 1009, 1777, 1889, 1979, 1997, 2677, 2699, 2767, 2789, 2879, 2897, 2969, 3779, 3797, 4567, 4657, 4679, 4967, 5399, 5557, 5647, 5669, 5737, 5849, 5939, 6277, 6299, 6367, 6389, 6547, 6563, 6569, 6637, 6653, 6659, 6673, 6763, 6947, 6983, 7177
Offset: 1

Views

Author

Osama Abuajamieh, Jan 16 2017

Keywords

Examples

			a(4) = 1777, since abs(digsum(1777)-2*L(1777)) = abs(A007953(1777)-2*A054055(1777)) is 8 and among the primes 1777 is the 4th element satisfying such condition.

Crossrefs

Subsequence of A280993.
Cf. A007953, A054055, A156753, A156979.

Programs

  • Mathematica
    Select[Prime@ Range[10^3], Abs[Max@ # - Total@ Rest@ #] == 8 &@ Reverse@ Sort@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)
  • PARI
    listA281170(k,{k0=8})={my(H=List(),y);forprime(z=prime(k0),prime(k),y=digits(z);if(abs(vecsum(y)-2*vecmax(y))==8,listput(H,z)));return(vector(#H,i,H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017
Showing 1-3 of 3 results.

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