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
Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010
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.
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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
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
Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 26 2010
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).
Redefined the variables in the definition -
R. J. Mathar, Jun 07 2010
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