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 1-2 of 2 results.

A178237 Smallest prime p of the form prime(n)+k^2 such that sum of digits(p) = prime(n).

Original entry on oeis.org

2, 3, 5, 7, 47, 157, 593, 919, 599, 66593, 46687, 396937, 467897, 467899, 6969647, 16499897, 367488959, 598095997, 2977884967, 4977866987, 2797986889, 58888728979, 58987779959, 679585896989, 4989996468997
Offset: 1

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Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010

Keywords

Comments

It is still an open problem if there exist infinitely many primes of form k^2 + d (d integer, no negative square).
For n<=4, k=0 suffices: e.g. prime(1)+0^2=2 = sum of digits(prime(1)), so a(n)=prime(n).

Examples

			a(13) = 467897 because its digitsum is 41 which is the 13th prime, it is of the form prime(13)+k^2 with k=684, and it is the least such prime.
		

Crossrefs

Programs

  • PARI
    sod(n) = {digs = digits(n, 10); return (sum(j=1, #digs, digs[j]));}
    a(n) = {k = 0; p = prime(n); while (! (isprime(q=p+k^2) && (sod(q) == p)), k++); return (q);} \\ Michel Marcus, Jul 26 2013

Extensions

a(5) corrected and sequence extended by D. S. McNeil, May 25 2010

A178371 The smallest prime p of the form j^3 + prime(n), such that the sum-of-digits of p equals prime(n).

Original entry on oeis.org

2, 3, 5, 7, 227, 229, 13841, 1747, 729023, 474581, 46687, 1259749, 37933097, 6434899, 14886983, 485587709, 2985984059, 2526569989, 56888939803, 60976889927, 60976889929, 879768685447, 8296386686867, 22597978779737
Offset: 1

Views

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 26 2010

Keywords

Examples

			n=1: 0^3 + prime(1) = 0+2 = 2.
n=2: 0^3 + prime(2) = 0+3 = 3.
n=3: 0^3 + prime(3) = 0+5 = 5. Next candidate with j>0 would be 6^3 + 7 = 223.
n=4: 0^3 + prime(4) = 0+7 = 7.
n=5: 6^3 + 11 = 227 = prime(49).
n=6: 6^3 + 13 = 229 = prime(50).
n=7: 24^3 + 17 = 13841 = prime(1636).
n=8: 12^3 + 19 = 1747 = prime(272).
n=9: 90^3 + 23 = 729023 = prime(58716).
n=10: 78^3 + 29 = 474581 = prime(39587).
n=11: 36^3 + 31 = 46687 = prime(4825).
n=12: 108^3 + 37 = 1259749 = prime(97168).
n=13: 336^3 + 41 = 37933097 = prime(2315164).
n=14: 186^3 + 43 = 6434899 = prime(440614).
n=15: 246^3 + 47 = 14886983 = prime(963902).
n=16: 786^3 + 53 = 485587709 = prime(25635800).
n=17: 1440^3 + 59 = 2985984059 = prime(143807568).
n=18: 1362^3 + 61 = 2526569989 = prime(122671100).
		

Crossrefs

Extensions

Redefined the variables in the definition - R. J. Mathar, Jun 07 2010
a(19)-a(24) from Donovan Johnson, Aug 09 2010
Showing 1-2 of 2 results.