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.

User: Charles U. Lonappan

Charles U. Lonappan's wiki page.

Charles U. Lonappan has authored 2 sequences.

A345072 Numbers k such that the sum of cubes of digits of both k and k-2 are primes.

Original entry on oeis.org

113, 115, 124, 148, 166, 184, 214, 223, 238, 256, 265, 283, 289, 298, 328, 337, 355, 364, 418, 463, 487, 496, 526, 535, 553, 568, 577, 586, 616, 625, 634, 643, 658, 694, 757, 784, 814, 823, 829, 847, 856, 874, 889, 928, 946, 964, 997, 1013, 1015, 1024, 1048, 1066
Offset: 1

Views

Author

Charles U. Lonappan, Jun 07 2021

Keywords

Comments

Numbers k such that k and k-2 appear in A225534.

Links

Crossrefs

Cf. A225534.

Programs

  • Mathematica
    q[n_] := PrimeQ[Plus @@ (IntegerDigits[n]^3)]; Select[Range[3, 1000], q[#-2] && q[#] &] (* Amiram Eldar, Jun 07 2021 *)

A344366 Integers k such that the sum of squares of digits of both k and k-1 are prime.

Original entry on oeis.org

12, 102, 111, 120, 160, 230, 250, 380, 410, 450, 520, 560, 720, 780, 830, 870, 1002, 1011, 1020, 1060, 1100, 1101, 1110, 1370, 1640, 1680, 1910, 1950, 1970, 1990, 2030, 2050, 2340, 2670, 2920, 3080, 3170, 3240, 3420, 3460, 3550, 3570, 3710, 3840, 3860, 4010
Offset: 1

Views

Author

Charles U. Lonappan, May 19 2021

Keywords

Comments

Integers k such that k and k-1 are both in A108662.
Terms are never prime. They cannot end in the digits 3,4,5,6,7,8,9.
If k is a term, phi(k) is divisible by 4.
The set of such numbers is infinite.

Examples

			12 is in the sequence because the sum of squares of digits of 12 is 5 and that of 11 is 2, and both 5 and 2 are prime numbers.

Links

Crossrefs

Cf. A108662.

Programs

  • Mathematica
    q[n_] := PrimeQ[Plus @@ (IntegerDigits[n]^2)]; Select[Range[2, 5000], q[#-1] && q[#] &] (* Amiram Eldar, May 19 2021 *)
  • PARI
    isok(k) = isprime(norml2(digits(k-1))) && isprime(norml2(digits(k))); \\ Michel Marcus, May 24 2021

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