A187744 -id:A187744 - cp's OEIS frontend

A117674 Prime numbers whose sum of digits is a triangular number.

3, 19, 37, 73, 109, 127, 163, 181, 271, 307, 433, 523, 541, 613, 631, 811, 1009, 1063, 1117, 1153, 1171, 1423, 1531, 1621, 1801, 1999, 2017, 2053, 2143, 2161, 2251, 2341, 2503, 2521, 3061, 3313, 3331, 3511, 3889, 4051, 4231, 4789, 4969, 4987, 5023, 5113

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), Apr 27 2006

			1999 is in the sequence because it is a prime number and the sum of its digits 1+9+9+9 = 28 is a triangular number.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A000040 and A187744.

Cf. A000217, A007953.

t={};Do[m = Total[IntegerDigits[Prime[n]]];If[IntegerQ[(Sqrt[8*m + 1]-1)/2],AppendTo[t, Prime[n]]],{n,700}];t  (* Jayanta Basu, Apr 27 2013 *)

isok(p) = isprime(p) && ispolygonal(sumdigits(p), 3); \\ Michel Marcus, Feb 08 2021

A062099 Triangular numbers whose sum of digits is a triangular number.

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 55, 78, 91, 105, 120, 136, 190, 210, 231, 253, 276, 300, 325, 406, 465, 528, 703, 780, 820, 861, 1081, 1176, 1225, 1275, 1540, 1596, 1653, 1711, 1770, 2080, 2211, 2346, 2701, 2775, 2850, 3003, 3160, 3403, 3486, 3570, 3741, 3828

Offset: 1

Amarnath Murthy, Jun 16 2001

			a(8) = 28 is a triangular number and the sum of digits 10 is also a triangular number.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Intersection of A187744 and A000217.

[ t: n in [0..90] | IsSquare(8*s+1) where s is &+Intseq(t) where t is n*(n+1) div 2 ];  // Bruno Berselli, May 27 2011

With[{trnos=Accumulate[Range[0,200]]},Select[trnos,MemberQ[trnos, Total[ IntegerDigits[ #]]]&]] (* Harvey P. Dale, Feb 26 2013 *)

{ for(m=0, 100, my(k=binomial(m+1,2)); if(ispolygonal(sumdigits(k),3), print1(k, ", "))) } \\ Harry J. Smith, Aug 01 2009

More terms from Erich Friedman, Jun 20 2001

A118488 Squares for which the sum of the digits is a triangular number.

Original entry on oeis.org

0, 1, 64, 100, 361, 1225, 2116, 3025, 5041, 6400, 10000, 17956, 18496, 21025, 23104, 26569, 29584, 32041, 36100, 38809, 47089, 54289, 58564, 59536, 63001, 68644, 69696, 77284, 82369, 87616, 88804, 94249, 110224, 117649, 122500, 128881, 130321

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 05 2006

			26569 = 163^2 is in the sequence because it is a square and the sum of its digits, 2+6+5+6+9 = 28, is a triangular number.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A000290 and A187744.

Cf. A000217.

Select[Range[0, 361]^2, IntegerQ @ Sqrt[8 * Plus @@ IntegerDigits[#] + 1] &] (* Amiram Eldar, Mar 24 2021 *)

isok(n) = issquare(n) && ispolygonal(sumdigits(n), 3); \\ Michel Marcus, Feb 27 2014

cp's OEIS Frontend

A117674 Prime numbers whose sum of digits is a triangular number.

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A062099 Triangular numbers whose sum of digits is a triangular number.

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Magma

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A118488 Squares for which the sum of the digits is a triangular number.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI